AN ABSTRACT OF THE THESIS OF Bryan M. O’Halloran for the degree of Master of Science in Mechanical Engineering presented on October 11, 2011. Title: METHODOLOGIES TO IMPROVE RELIABILITY ENGINEERING IN EARLY DESIGN Abstract approved: ___________________________________________________ Robert B. Stone ___________________________________________________ Irem Y. Tumer This thesis is the summation of two publications with the motivation to move reliability analysis earlier in the design process. Current analyses aim to improve reliability after components have been selected. Moving specific analyses earlier in the design process reduces the cost to the designer. These early design analyses provide information to the designer so that critical design changes can be made to avoid failures. The first presents failure rates for function-flow pairs. These function-flow failure rates are used in the Early Design Reliability Method (EDRM) to calculate system level reliability during functional design. This methodology is compared to the traditional reliability block diagram for three examples to show its usefulness during early conceptual design. Next, an extension to the Function Failure Design Method (FFDM) is presented. A more robust knowledge base using Failure Mode/Mechanism Distributions 1997 (FMD-97) has been implemented. Then failure rates from Nonelectric Parts Reliability Data (NPRD-95) are added to more effectively determine the likelihood that a failure mode will occur. The proposed Functional Failure Rate Design Method (FFRDM) uses functional inputs to offer recommendations to mitigate failure modes that have a high likelihood of occurrence. This work uses a past example where FFDM and Failure Modes and Effects Analysis (FMEA) are compared to show that improvements have been made. A four step process is presented to show how the FFRDM is used during conceptual design. © Copyright by Bryan M. O’Halloran October 11, 2011 All Rights Reserved Methodologies to Improve Reliability Engineering in Early Design by Bryan M. O’Halloran A THESIS submitted to Oregon State University in partial fulfillment of the requirements for the degree of Master of Science Presented October 11, 2011 Commencement June 2012 Master of Science thesis of Bryan M. O’Halloran presented on October 11, 2011. APPROVED: _____________________________________________________________________ Major Professor representing, Mechanical Engineering _____________________________________________________________________ Co-Major Professor representing, Mechanical Engineering _____________________________________________________________________ Head of the School of Mechanical, Industrial, and Manufacturing Engineering _____________________________________________________________________ Dean of the Graduate School I understand that my thesis will become part of the permanent collection of Oregon State University libraries. My signature below authorizes release of my thesis to any reader upon request. _____________________________________________________________________ Bryan M. O’Halloran, Author PUBLICATION THESIS OPTION This thesis is presented in accordance with the Manuscript Document Format option. Two manuscripts are provided. The first was published in the 2011 International Design Engineering Technical Conference and the second was accepted for publication to the 2011 International Mechanical Engineering Congress and Exposition. ACKNOWLEDGEMENTS I express my gratitude and appreciation to Dr. Robert Stone. His consistent support has allowed myself to develop and has provided an optimal environment for research. I would equally like to thank Dr. Irem Tumer for her insightful suggestions and guidance in conducting this research. Her valuable support has steered this research to always remain relevant. I would like to thank David Jensen for his insightful feedback. His paper revisions were critical in the development of this research. I would like to thank all members of the Design Engineering Lab for providing a great environment to conduct research. Their feedback during weekly meeting had a tremendous impact on continuing to keep this research moving forward. Last, I would like to thank Deanna O’Halloran, my wife, Logan O’Halloran, my son, and Mike and Jennifer O’Halloran, my parents, for their continued support for my goals. This research was funded in part by DARPA (Subaward to FA8650-10-C-7079 with Palo Alto Research Center). TABLE OF CONTENTS Page INTRODUCTION....................................................................................................1 ABSTRACT..............................................................................................................5 INTRODUCTION....................................................................................................5 BACKGROUND......................................................................................................6 The Function Failure Design Method............................................................10 Normalized Method for Archived Data Sets Using the Heaviside Function.10 RESEARCH METHOD..........................................................................................11 Component Failure Rate Data Source............................................................11 Repository Data.............................................................................................12 Applying Rules Using the Heaviside Function.............................................14 Function-flow Failure Rates..........................................................................14 RESULTS................................................................................................................16 Proposed Methodology for Calculating System Reliability..........................16 Exploring New Functions in the Functional Model......................................17 Methodology Example Using Real Products.................................................18 CONCLUSION.......................................................................................................22 FUTURE WORK....................................................................................................23 ACKNOWLEDGEMENTS....................................................................................23 APPENDIX.............................................................................................................24 ABSTRACT............................................................................................................27 INTRODUCTION..................................................................................................27 TABLE OF CONTENTS (Continued) Page BACKGROUND....................................................................................................28 Functional Modeling......................................................................................28 Function Failure Design Method...................................................................29 Risk in Early Design......................................................................................30 Failure Rates, Modes, and Mechanisms........................................................31 Failure Modes and Effects Analysis..............................................................32 RESEARCH APPROACH......................................................................................34 Component Failure Rate Data Source...........................................................34 Failure Modes and Mechanisms Data Source...............................................35 Repository Data.............................................................................................37 Converging Data Using Matrix Multiplication..............................................38 RESULTS................................................................................................................39 Failure Mode Data.........................................................................................39 Function Failure Rate Design Method...........................................................42 Design Recommendations.............................................................................44 Failure Mode Likelihood...............................................................................46 CONCLUSION.......................................................................................................48 FUTURE WORK....................................................................................................48 ACKNOWLEDGEMENTS....................................................................................49 APPENDIX.............................................................................................................50 CONCLUSION.......................................................................................................52 VITA.......................................................................................................................55 REFERENCES.......................................................................................................56 LIST OF FIGURES Page 1: Series Structure of a Reliability Block Diagram....................................................8 2: Parallel Structure of a Reliability Block Diagram..................................................9 3: Function-Component Matrix................................................................................13 4: Methodology to Calculate System Reliability......................................................16 5: Reliability Results for the Electric Toothbrush....................................................19 6: Reliability Results for the Electric Bread Slicer...................................................20 7: Reliability Results for the Bottle Capping Machine.............................................21 8: Red Database Population......................................................................................30 9: Function-Component Matrix Snippet...................................................................38 10: Function-Failure Mode Matrix Snippet..............................................................40 11: Failure Mode Data for Secure Solid...................................................................41 12: Functional Model for Portable Air Compressor.................................................42 13: FFDM Step #1 Snippet.......................................................................................43 14: FFDM Step #2 Snippet.......................................................................................43 15: FFDM Step #3 Snippet.......................................................................................44 LIST OF TABLES Page 1: Example Using Functional Basis Terminology...................................................29 2: FFDM Example for a Portable Air Compressor..................................................45 3: Additional Recommendations for the Portable Air Compressor.........................46 4: Failure Rates of Failure Modes for Portable Air Compressor.............................47 LIST OF DEFINITIONS Failure: Undesirable loss in functionality during a specified life Failure mode: Observable consequence of a failure or change in behavior from a failure Failure mechanism: Physical process which causes a failure Function: What the system does to accomplish a task Component: Solution to a function which has physical form Occurrence: A single data point based on a relationship Design Repository: Database of product information and design tools Constant failure rate: Number of failure of the design divided by the operation time of the design Failure Probability: Probability that a failure will occur under the stated assumptions of the analysis 1 METHODOLOGIES TO IMPROVE RELIABILITY ENGINEERING IN EARLY DESIGN INTRODUCTION The field of Reliability Engineering is concerned with managing, studying, evaluating, and mitigating failures in design and manufacturing. Using reliability engineering analyses in design can improve availability, reduce maintenance and cost, and improve safety for the customer. In general, reliability of a design is viewed separate from functionality and requires independent analyses. These analyses exist mostly for the later stage of design, once a computer model or physical prototype has been developed. There are many reasons why this is true, for example failure occurrence data is recorded for failed components, not lost functionality. It is also impossible to evaluate properties such as stress for functionality; however, this is common practice for components. The early stages of design lack formal methods in reliability engineering. This research produces a means to address this need. Traditional reliability engineering analyses have been used to increase safety and reduce the likelihood of failures for many years. As the field of reliability engineering grows, so do the efforts to increase its presence in early design. This research has focused on moving reliability analyses into the functional design stage. Functionality is the stage where the voice of the customer is captured to describe what the product must do. For this reason, failure can be defined as the loss of functionality [1]. When a design stops working the way a customer prefers, it has failed. Since we design for functionality, methodologies in this research has been formulated to provide designers the capability to perform reliability analyses directly after generating a functional model. Functional modeling is performed at the conceptual stage of design before any components have been selected [2]. There are a variety of reasons to increase the presence of reliability engineering in early design. One reason is that offers the designer cost-effective choices. Later in the design process choices become increasingly expensive and complicated to implement. The goal of this research is to provide the designer with 2 more knowledge from which these important decisions can be made. Knowledge, in the form of methodologies, guides the design toward a more reliability solution. Each of the two methodologies presented here uniquely contribute during the design process. In the first manuscript a methodology is developed to calculate function-flow failure rates using component failure rates. This process uses the Design Repository for function to component mapping, a Heaviside function to eliminate noise in the data, and simple computations and logic statements to arrive at the function-flow failure rates. The result is a minimum, maximum, and weighted average function-flow failure rate. This process can be reproduced using different components, component failure rates, functional languages, occurrence data, or Heaviside rules. Similar to component failure rates, this data can be used to select reliable function-flows during the design process, or can be employed in traditional reliability engineering analyses such as Functional Reliability Block Diagram (FRBD). A methodology is presented to calculate system level reliability using an FRBD style approach. Within this methodology, the step mitigate failure rates is used as a design tool to increase the reliability. In the second manuscript, improvements are made to an existing methodology, namely the Function Failure Design Method (FFDM) [3]. New data is added to determine a relationship between functions and failure modes is increased and an additional step is added to convert occurrence data to rate data. Within this process, the Design Repository was used to acquire the link between functions and components. Failure Mode/Mechanism Distribution (FMD-97) [4], a comprehensive manual from the Reliability Information Analysis Center (RIAC), was used to generate a matrix linking components to failure modes. Component failure rates are used to convert occurrence data to rate data. This allows the failure modes to be prioritized by the likelihood of occurrence. The rate data in the function to failure mode matrix was calculated to be used in the Function Failure Rate Design Method (FFRDM), however the process to calculate the data can be redone using different initial data. 3 Also in the second manuscript, FFRDM is presented to provide critical failure information in the conceptual design stage to reduce the likelihood of failure. This data shows the designer the likelihood that a function-flow will fail in a specific failure mode. FFRDM is shown to expand on the Function Failure Design Method (FFDM) to prioritize failure modes, making the decision on which failure mode to mitigate. A significant amount of data has been added to expand the knowledge base to provide more robust results. FFRDM was tested on the design of a portable air compressor to show improvements in prioritizing the failure modes. This was a previous example where FFDM was compared to failure modes and effects analysis (FMEA). It is shown that improvements in FFDM have been accomplished by determining additional failure modes which were overlooked in the original comparison. In this research FFRDM is discussed as an alternative to FMEA. However, it should also be noted that FFRDM can supplement a portion of FMEA. For new designs, FMEA generally requires guessing failure modes. FFRDM can first provide a list of failure modes for new designs based on historical data. Second, it can accurately quantify the probability of occurrence. The output of FFRDM should to be converted to a 1 - 10 scale for compatibility with FMEA. Performing reliability analysis at the conceptual level of design offers the power of risk informed decision making to the designer. As the design process continues it becomes increasingly expensive to make design changes. Providing an analysis that can mitigate this problem at the conceptual level may significantly reduce the likelihood of costly failure events. 4 Early Design Stage Reliability Analysis Using Function-flow Failure Rates Authors Bryan M. O’Halloran 100 Dearborn Hall Email: ohallorb@onid.orst.edu Robert B. Stone Ph.D 406 Rogers Hall Email: rob.stone@oregonstate.edu Irem Y. Tumer Ph.D 408 Rogers Hall Email: irem.tumer@oregonstate.edu Proceedings of the ASME 2011 International Design Engineering Technical Conferences Design Theory and Methodology Conference IDETC/CIE 2011 August 28-31, 2011, Washington D.C., United States of America 5 ABSTRACT In this paper, failure rates for function-flow pairs are presented. This data creates an opportunity for the designer to move reliability analysis earlier in the design process. The function-flow failure rates can be used to make design decisions before components are selected giving the designer increased knowledge to explore alternative options. A reliability block diagram approach has been adopted to evaluate the reliability of three designs at both the functional and component level. The results show that the bounds from the functional reliability overlap those of the component reliability. 1. INTRODUCTION Traditional reliability engineering techniques have been used to increase safety and reduce the likelihood of failures for many years. As the field of reliability engineering grows, so do the efforts to increase its presence in early design. The early design phase has the distinct advantage of offering the designer cost-effective choices as opposed to later in the design process. The premise of this research is to provide the designer with more knowledge to which these important decisions can be made. Data, which can be used in a variety of ways, is presented here in the form of function-flow failure rates. Similar to component failure rates, this data can be used to select reliable function-flows, or can be employed in traditional reliability engineering analyses such as Functional Reliability Block Diagram (FRBD). Specifically, a methodology was proposed to calculate the system level reliability using FRBD and function swapping to show the usefulness of the data. The scope of this research is to first present minimum, maximum, and weighted average function-flow failure rates. This information is based on collected data and is not intended to demonstrate failure modes or mechanisms. Second, a design methodology is introduced to calculate system level reliability at the functional level. 6 2. BACKGROUND This section provides a survey of related research including several traditional and non-traditional reliability engineering techniques, FFDM, and the use of a normalization method to account for variations in archived data sets. Traditional risk and reliability analysis techniques exist primarily to move failure assessments into the earlier stages of design. These efforts look at system components, critical events, and system characteristics to assess risk and reliability during the design phase. Reliability engineering techniques can help engineers better meet the needs of customers. In general, customers want two things out of a product. First they want the product to function properly according to their needs, and second they want it to function reliably. Assessing reliability during the design stage helps drive designs to function reliably. In reliability engineering failure is defined as a design not functioning as originally intended for a given life in specific operating conditions [1]. There are several methods used to increase the reliability of the design including Failure Modes Effects and Criticality Analysis (FMECA), Event Tree Analysis (ETA), Fault Tree Analysis (FTA), and Reliability Block Diagrams (RBD). Each of these analyses accomplishes a different goal and are each used during the design process. The goal of FMECA is to identify, evaluate, and prevent critical component failures [5]. Critical components are determined by the risk priority number (RPN). Components with high RPN values receive a recommended action and schedule to resolve their being critical. The FMECA analysis starts by identifying a list of components and their potential failure modes. The RPN value is the product of three variables; occurrence, severity, and likelihood of detection. Occurrence refers to the likelihood that the failure will occur, severity is how bad the failure is, and likelihood of detection is how hard it will be to detect. From the list of potential failures, the occurrence, severity, and likelihood of detection are scored on a scale of 1 to 10, resulting in an RPN value of 0 to 1000. The usefulness of FMECA as a design tool is to look at the RPN values relative to each other and determine which components 7 needs action taken and which do not. From this analysis, the designer can determine the critical components of a system and make design changes accordingly. A variety of software tools and methodologies exist to improve and automate FMEA including FMEA streamlining [6], WIFA [7], FLAME [8, 9], CFMA [10], and Advanced FMEA (AFMEA) [11, 12]. Although, these automated tools are not capable of predicting failures. ETA is a bottom-up approach to system reliability analysis and is used to determine the likelihood of an outcome based on an accidental event [13]. This shows the designer end failure states that have a high probability of occurring. ETA uses the probability of different failures occurring in the system combined with the probability of safety barriers to determine the final state probabilities. A safety barrier is anything in the design used to resolve a failure in the chance that is occurs. This would, for example, be a ceiling sprinkler system in the event of a building fire. ETA is computationally simple to perform, although depending on the number of accidents analyzed and the level of detail explored, it can be lengthy. The usefulness of this method is in the ability to determine accurate probabilities for events and barriers, then make design decisions to increase the system reliability. It can be difficult to accurately define the probabilities of events and barriers [14]. Design decisions cannot be made with confidence unless these probabilities are well accepted. A fuzzy logic has been developed to account for this. Specifically it determines the uncertainty in the probability of failures and defines a qualitative impact of certain outcomes. This also can be a useful tool for decision making. FTA is a top-down approach to reliability analysis which begins with an undesirable state and determines the initial cause [15]. Events that could cause the undesirable event are listed in the row below it. Beneath each of the row 1 events are row 2 events. This continues until a basic event is reached where there does not exist a further occurrence to cause it. Between each row are the connections and logic gates that define each of the relationships. In general, two types of logic gates are used; “AND” and “OR”. AND gates require that each of the events in the next row must occur for the event to occur. OR gates only require a single event in the next row to 8 occur for the higher level event to occur. Probabilities are assigned to each event so the probability of the top failure event can be determined. The top event probability is simple to calculate. In order to perform FTA, the system must be well understood so everything is captured. RBD are another method used to determine system level reliability of a design during the design stage [16]. This is useful when requirements dictate the level of reliability a design can have. For complex systems, these diagrams are useful as a visual tool to see where failures will occur. They also make computation simple to perform. Although, the diagram itself is not used to show the architecture of the system, but instead only to provide graphical information on how it fails. Meaning that if components are connected in the RBD, this does not necessarily mean they are in the physical design. In general, there are two structure types; series and parallel. These refer to the a theoretical path of working components that a design can take to accomplish its overall function. If the structure is series, there is only a single path and all components along that path must function properly or the design fails. C1 C2 C3 FIGURE 1: Series Structure of a Reliability Block Diagram If the path splits into a parallel structure, any path is sufficient to accomplish the function. In other words, there must always exist a path from start to finish of properly functioning components in order for the design to be functioning. For example, two motors running in parallel to drive the same component where either motor meets the power requirement for the overall system. The system can still function if one of the motors fails. 9 C1 C2 C3 FIGURE 2: Parallel Structure of a Reliability Block Diagram Failure rate data for each component, given by the variable (λ), is needed to calculate the reliability. Also, a time value (t) is needed since reliability is time dependent. For electromechanical designs with constant failure rates it can be assumed that the reliability behaves according to an exponential distribution. Equations (1-3) calculate the system level reliability using an exponential distribution assuming failures are independent. !!"#$"! ! ! !!! !! !!"#"$$%$ ! ! ! !! ! ! !!! !! (1) ! !!! ! ! !! (2) (3) These are useful to determine the system level reliability to meet design criteria. The designer can also use the RBD to add redundancies that increase reliability. Problematic areas become easy to identify in a large design using this technique. A disadvantage to generating RBD is the high user workload. A variety of software tools have automated this process including Reliasoft BlockSim – Version 10 6.5.2, ARINC Raptor – Version 7.0.07, and Relex Software Reliability Block Diagram [17]. Less common methods such as Synergetic Reliability Prediction (SYRP) are also used during the design process to predict later life failure [18]. This method has been shown to be accurate but requires an in-depth and lengthy analysis and expert knowledge to perform. Work has been done to estimate the probabilities of failures using the mean time between failure, but is a lengthy process and requires a significant amount of work to understand [19]. 2.1. Function Failure Design Methodology FFDM is a structured formulation of the function-failure analysis method introduced by Tumer and Stone, and is used to perform failure analysis in the conceptual design stage [20]. This method also aids the designer by using a functionbased concept generator approach which helps streamline the design process. FFDM is a start-to-finish design method which utilizes knowledge bases that link product function to failure modes and product function to design concepts. The knowledge base data is archived in the form of a function component matrix and reduces the need for the designer to have a large intellectual knowledge base. FFDM has several advantages over other reliability engineering methods including reduced high user workload, using archived failure knowledge base, being usable during functional design, using a formalized failure language, and is practical for electrical and mechanical systems [21]. However, FFDM lacks a strong component to failure mode relationship, limiting the usefulness of the results. 2.2. Normalization Method for Archived Data Sets Using the Heaviside Function An archived set of product data inevitably contains a certain amount of variations. This would, for example, include data completeness and correctness. Normalization methods provide a systematic way to lessen the impact of data variations. 11 McAdams and Wood used a norming method to develop a quantitative designA graphical by-analogy metric based on the functional similarity of productsFig. [22].3 This norming interpretat similarity projection Fig. 2 Normalization process: … original function-product method uses a pair of rules to„aaccount for differing product customer needs importance matrix !, „b… equalizing product importance, „c… determining complexity. Data was using productfor function matrix for easy average and number of functions per represented product, and „d… ascaling product complexity to get the final matrix N Once manipulation and data structuring. Each matrix element is the product of 2calculated, ratios; the this projectio This projection is denoted with a number of functions in a particular product over the average number of functions a product vec product betweenin the is based on the numb product and the average customer needs rating over the customer measure needs for a) particular The number of functions in the jth product is products and the customer import words, this projection provides m of a design. This value is then used to select analogous designs. similarity. It is a simultaneous m ! j! H# $i j %. (4) and customer importance. A grap The Heavisidei!1 function is used as a conditional binary multiplication see jection is shown in Fig. 3. In this The average number equation 4. Inof thefunctions case that aisspecific cell value is equal, or not equal, to is zero the value space shown for the functions s rotation, and position solid. Pro m none, or zero. To determine the average number of functions of the Heaviside becomes 1 Product B and the projection o ! ¯ !Heaviside function H # $ i j was (5) row and column. % . summed across each for a product the shown. This represents the simil n i!1 j!1 products. H is a Heaviside function defined as For clarification of the formula representative numerical example when x&0 {11 !ℎ!" ! ≥ !} uct vectors for Product A an H (6) x ! % ! ! = # . (4) gives (0.22,0.44,0.87)!(0.54,0.71 {00 !ℎ!" ! < !} when x!0 #0.87"0.54!0.55 In the above equations, n is the number of products, and m is the A matrix of these projections i total number of different functions for all products. *!N Figure3.2 shows the complete normalization process for some RESEARCH APPROACH hypothetical set of products. The top left matrix in the figure #a% is N is the matrix of unity-normaliz matrix This'.section presents the to method for then determining failure the original Moving from left right and down inthe function-flow Each element, ) i j , is the projecti the figure, firstThe the matrix is adjusted to equalize product rates. steps include finding component failureimporrates, mapping to product.functions * is the product similarit tance #b%. This is done be multiplying $ i j by the scaling coeffi- cation to form the product simi validating theThen data,this andterm calculating the minimum, maximum, and cient ( ¯( /components, ( j ) as computed from '. is multiplied by technique Taylor +15, used to dete the scaling coefficient ¯ ) as determined weighted average( ! function-flow failure rates.from the matrix discussion on internet newsgroup j /! shown in #c%. The result is the final matrix N shown in #d%. The sign teams. The product projectio functions in the N matrix are comparable for importance from dates for finding meaningful desig product to product. 3.1. Component Failure Rate Data Source functional level. product. Norming this data gives the designer a way to calculate the similarity metric " "" ! Asasthis Nonelectric Parts Reliability Data (NPRD-95) [23] was used the similarity source of metric is com 3.3 Computing Similarity. The elegance and power of this need to be stored and accesse vector representation maderate clear the reference development the that the componentare failure data.inThis is anofongoing effort to collect and of this method are customer nee quantified product similarity metric. Using the matrix representaThis approach provide high volumes of data from of sources including both militarygreatly and reduces the tion, N, the entire domain of products can abevariety reviewed for funcfor locating similar products. Th tional similarity. The This product vectors generated from Eq.manuals, #1% are government commercial. specifically includes warranty sponsored renormalized so that their norm is 1. After scaling, the inner prod- allow the generation of data to b studies, published papersvectors and reports, databases, and military currently insystems. progress +16,. uct of the normalized product for each combination of maintenance products is calculated. Forming the inner product between a product a and a product b, a!b, gives the projection of product a on product b. Forming the inner product of a product with itself #the Table 3 Product vectors completely similar product% gives a value of 1. Forming the inner 12 From the previous publication, NPRD-91, 56% more data has been acquired. A strong emphasis was put on data quality during the collection phase. This was done by ensuring completeness of data, consistency of data, equipment population tracking, failure verification, and characterization of operation histories. Often data is discarded if it does not meet quality standards. Also, this document did not indicate failure modes or mechanisms. Failure, as observed in NPRD-95, is classified generically under solving the symptoms of the failure. A part failed if, when it was replaced, the failure symptoms were not present anymore. Comprehensive indices are provided for background on the parts and sampling. These include the component manufacturer, model or part number, nominal performance specifications specific to each part, population tested, number of operation hours, and number failed. The operating hours and number of parts failed is used to generate failure rates for both specific components and component classes. For example, a failure rate is provided for a specific type of actuator, then a combined failure rate is given for the actuator class. The failure rate for each component class is the sum of the total components failed for that class divided by the sum of the operating hours for each component in that class. Calculating both types of data lets the user employ the data at a generic or specific level. 3.2. Repository Data The Design Engineering Lab Repository (http://designengineeringlab.org/ delabsite/repository.html) at Oregon State University was used for function component mapping and data structuring. A tool within the repository has the capability to generate Microsoft Excel spreadsheets based on the designer’s intent. For the purpose of this research, a function-component matrix (FCM) was created with function-flows and using the component naming. The FCM is used to capture the relationship between the functions and component naming terms. Structurally, the FCM lists component naming terms across the first row as column headers and function-flow pairs down the first column as row headers. Elements of the matrix are then filled with the occurrences of the number of 13 times a function is solved by a component. Initially there are 164 components listed and 731 function-flows. The total number of occurrences is 16,365. Function(Component-Matrix Failures/Mhours 192.0795 x 0.1949 2.2727 15.4501 0.1624 x x Generated-On:-Wed-Jan-26-22:44:46-PST-2011 converter conveyer coupler cover crank digital-display diode distributor convert-pneumatic-to-status 0 0 0 0 0 0 0 1 convert-pneumatic-to-translational 0 0 0 0 1 0 0 0 convert-radioactive/nuclear-to-chemical 0 0 0 0 0 0 0 0 convert-radioactive/nuclear-to-control 0 0 0 0 0 0 0 0 convert-radioactive/nuclear-to-electrical 0 0 0 0 0 0 0 0 convert-rotational-to-acoustic 0 0 0 0 0 0 0 0 convert-rotational-to-electrical 0 0 0 0 0 0 0 0 convert-rotational-to-hydraulic 0 0 0 0 0 0 0 0 convert-rotational-to-mechanical 0 0 0 0 0 0 0 0 convert-rotational-to-pneumatic 0 0 0 0 0 0 0 0 convert-rotational 0 0 0 0 0 0 0 0 convert-rotational-to-status 0 0 0 1 0 0 0 0 convert-rotational-to-translational 0 0 2 0 0 0 0 0 convert-signal-to-status 0 0 0 0 0 0 0 0 convert-signal-to-visual 0 0 0 0 0 1 0 0 convert-solar-to-chemical 0 0 0 0 0 0 0 0 convert-solar-to-electrical 2 0 0 0 0 0 0 0 convert-solar-to-status 0 0 0 0 0 0 0 0 convert-solar-to-thermal 1 0 0 0 0 0 0 0 convert-solid-to-chemical 0 0 0 0 0 0 0 0 convert-solid-to-liquid 0 0 0 0 0 0 0 0 convert-solid 1 0 0 0 0 0 0 0 convert-solid-to-solid(solid 0 0 0 0 0 0 0 0 convert-status-to-analog 0 0 0 0 0 0 0 0 convert-status-to-control 0 0 0 1 0 0 0 0 convert-status-to-electrical 0 0 0 0 0 0 0 0 FIGURE 3: Function-Component Matrix The example FCM snippet in Figure 3 shows convert rotational to translational being solved twice by the coupler. Zeros in the matrix indicate that there is no observed relationship in the repository of the particular function-flow and component. The component naming terms along the first row of the FCM are specifically defined [24]. These terms line up with the component classes listed in NPRD-95. The data was translated over from NPRD-95 and entered into the Excel spreadsheet. For names that did not match identically, the component naming definitions were used to justify that the data was correctly being transferred. For components without data, an X was entered for the component failure rate. 14 3.3. Applying Rules Using the Heaviside Function As a means to take the failure rate listed for a specific component to individual function-flows, it is important to avoid letting particular components dominate the data. For example, a nozzle has solved couple solid three times out of 2045. Since the nozzle has a high failure rate of (718 failure per million hours), couple solid will also have a high failure rate. However, the nozzle solves the function couple solid in this particular case, it is an exception rarely observed. The Heaviside function has been used as a way to assign an importance rating. The occurrence data must meet the requirements of the Heaviside function according to the following rules. Rule 1: A function-flow must be solved at least 3 times. This requires that any function will either see a variety of failure data because it is solved by different components, or has been solved by the same component at least three times. Rule 2: A cell must contain greater than 1% of the total occurrences for the entire component. For a component that has 100 occurrences, a function-flow must be solved more than once by this component or the failure rate is not inherited. This rule will eliminate function-flows from inheriting failure rates when their solution is an exception to how the component is generally solved. 3.4. Function-flow Failure Rates The process to use the data to determine the functional failure rates after applying the rules is described here. The process to determine the weighted average differs from that of the minimum and maximum and is described in the following paragraph. 15 The matrix resulting from the Heaviside calculation, named T2, was used as a starting point to determine the weighted average failure rate. Another matrix was formulated to prepare for the final calculations which used a logic test to determine if a cell has an occurrence greater than zero, then if that particular component had failure rate data. These preparation steps avoid mathematical and programming errors such as adding up X’s or dividing by zero. The following line of code tests is a cell contains an X, if the sum of a row is greater than zero, if a component failure rate is greater than zero, and if the failure rate is listed as X. =IF('T2'!B31>0,IF('T2'!$FK31>0,IF('FCM (Mhours) 2'!E$4>0,IF('FCM (Mhours) 2'! E$4="x","x",('T2'!B31*'FCM (Mhours) 2'!E$4)),"x"),"x"),"x") When the final statement is false and the first three are true, the component failure rate is multiplied by the occurrence. These values, across a row for a specific functionflow, were summed and divided by the total number of occurrence for the same function-flow. The following line of code completes the calculation for the weighted average function-flow failure rate. =IF(SUM('T3'!B35:FI35)>0,SUM('T3'!B35:FI35)/'T2 (2)'!$FK35,"x") The total occurrences were those that occurred when the component also had failure data. This way, components that were not counted in the summation were also not counted in the total number of occurrences. This calculation determined the weighted average function-flow failure rates. To determine the minimum and maximum failure rates, the matrix T2 was converted into a binary matrix containing values of only 1 and 0. A binary matrix is used only to show that there exists a relationship between a function-flow and a component. This eliminates the occurrence information since it does not capture the one to many relationship between function-flow and component. This is due to how the FCM is constructed. A component is listed, then the occurrences for it solving each 16 function-flow are listed in the same column. This data represents only when one or more functions are solved by the same component. It does not reflect the occurrences when a single function is solved by multiple components. In this instance, each component that solves a part of this function-flow would list a value of 1 for that function-flow in its own column. This results in the solution for that function-flow adding up to greater than one. 4. RESULTS This section presents the results of the function-flow failure rates. This data is presented in a complete table in Appendix A. An RBD style failure analysis has been adopted for validation. Both RBD’s and the proposed methodology are used to calculate system level reliability of each design to evaluate the usefulness of the calculated data. This comparison is done using three different designs. 4.1. Proposed Methodology for Calculating System Reliability This process involves five steps. Figure 4 provides an overview and flowchart for the proposed methodology. This analysis begins by generating a complete functional model. All functions and flows necessary to satisfy the customer needs must be present. Function-flows are then restructured to reflect the FRBD instead of the functional model. Each functionflow is placed in a box, then the designer must reason about its role in the overall system failure. If the function-flow fails, will the entire design fail, or is there an additional functionality that would keep this from occurring? In the case where there is not, this function-flow is in series in the FRBD. If there is additional functionality, these two function-flows are in parallel. Next, data is pulled out of Appendix A for each function-flow. All values including minimum, weighted average, and maximum should be recorded. Functionality can be added or functions can be swapped to reduce the combined failure rate. This is explained in section 4.2. Equations (1-3) are then used to calculate the reliability in the same manner as a traditional RBD. This should 17 be individually calculated for the minimum, weighted average, and maximum failure rate. Generate Functional Model Reformat Using Reliability Block Diagram Structure Gather Failure Rate Data Mitigate Failure Rates Perform Reliability Block Diagram Calculations FIGURE 4: Methodology to Calculate System Reliability 4.2. Exploring New Functions in the Functional Model Exploring functions to reduce the combined failure rate using this framework is done one of two ways. First, functions can be swapped out for new functions which have lower failure rates and second functions can be added using a parallel structure in the RBD. This data can be used to let the designer know when to explore different functions in the functional model. Certain function-flows with high failure rates can be exchanged with others to generate alternate final designs. This leads to a component with a low failure rate solving the function-flow. Since functional modeling is performed at an abstract level and problem statements are often not well defined, new functions can be explored in place of others to solve the same blackbox function. Another option when the basic functionality is strictly required by the product is to add mitigating functions for the high failure rate functions. For example, if the 18 function convert pneumatic energy to mechanical energy has an unacceptable failure rate and is known to historically fail from overheating, additional functionality to mitigate this failure can be used. This could be distribute thermal energy or export thermal energy. In the RBD this would reduce the final failure rate because the new functionality would be in parallel with convert pneumatic energy to mechanical energy. In reality, this would be adding a heat sink which is commonly done to relieve heat from a system and reduce the likelihood of failure. 4.3. Methodology Example Using Real Products As a way to validate the proposed methodology using the function-flow failure rates, examples have been provided. Three products each with functional models (FM) and configuration flow graphs (CFG) were found [22, 25]. An RBD approach has been adopted to measure the reliability of each CFG. These traditional RBD were constructed with component failure rates from NPRD-95. In the reliability calculation an exponential distribution of failure rates was assumed. Since products have relatively few components and no redundancies, it was determined that the RBD structure was entirely in series. That is, if any component fails, the overall function is no longer accomplished. In order to use the functional failure rates, the proposed methodology is used. Again, the three products are relatively simple and do not contain any parallel structures or redundancies. For more complex systems, redundancies would be present in the RBD structure resulting in a combination of parallel and series structures. The three products evaluated were an electric toothbrush, an electric bread slicer, and an automated bottle capping machine. Each product had an overall reliability calculated from the traditional RBD, and for comparison purposes a minimum, maximum, and weighted average reliability using the proposed methodology. Time values were selected to reflect a reasonable operation for each. The first product explored was an electric toothbrush. The blackbox function of this product is to separate solids. The results in Figure 5 show that the average reliability at 1,000 hours is 95%. The proposed methodology results were compared 19 relative to the traditional RBD. The maximum is less than 1% higher while the minimum is significantly lower, only 7% reliable at 1,000 hours. The weighted average is 4% lower. This result is expected based on the components and functionflow pairs present in the design. The largest component failure rate seen in the product was the link with a value of 10.97 failures per million hours and the lowest was the housing at 0.013 failures per million hours. The function with the greatest failure rate was export solid with a value of 717 failures per million hours. The minimum was found in the function-flow import solid at 0.0018 failures per million hours. Electric(Toothbrush( Reliability& 95.1%& 95.9%& 91.1%& 19.5%& CFG& Maximum& Average& Minimum& FIGURE 5: Reliability Results for the Electric Toothbrush Four function-flows and two components were not included in the reliability calculations. These components included electric wire and guiders. Electric wire does not have failure rate data in NPRD-95. The rate for guiders was excluded because the function-flows that it maps to does not have data. These function-flows include convert rotational to translational mechanical energy and transfer translational mechanical energy. Similarly, transfer electrical energy was excluded as a result of the missing electrical wire data. Mix solid to mixture did not receive failure rate data as a result of not passing the rules discussed previously. This is one of many functions accomplished by the brush component on the toothbrush. The brush was left in the calculation as were the other function-flows that is solves. 20 The next product tested was an electric bread slicer. This product also separates solids, but uses a different variety of components to accomplish its blackbox function. The reliability found from the RBD at 1,000 hours was 96%. The results from the proposed methodology show the minimum, maximum, and weighted average were found to be 85%, 99%, and 96% respectively. The results for this product show a strong correlation between the traditional RBD and the weighted average from the proposed methodology. Components in the electric bread slicer with the highest and lowest failure rates were the handle (11.01 failures per million hours) and an electric switch (0.82 failures per million hours). For the function-flows these were both import human energy and actuate electrical energy (25.81 failures per million hours) and import electrical energy (0.0021 failures per million hours). Bread&Slicer& Reliability& 96.2%& 98.7%& 96.5%& 85.0%& CFG& Maximum& Average& Minimum& FIGURE 6: Reliability Results for the Electric Bread Slicer Two components and five function-flows were not included in the reliability calculations. Both blade and electric wire are without failure rate data in NPRD-95 and therefore their corresponding function-flows were not included in the calculation. These function-flows include transfer electrical energy, import solid, secure solid, separate solid, and export solid. The third product tested was an automated bottle capping machine. This product imports a bottle on a belt, grabs it with a clamp, caps it, then exports the 21 capped bottle. The blackbox function of this product is to couple solids. The reliability of the bottle capping machine at 10,000 hours was 61%. The results from the proposed methodology for the minimum, maximum, and weighted average were found to be 7%, 76%, and 49% respectively. The components with the highest and lower failure rates were a handle (11.01 failures per million hours) and an electric conductor (0.019 failures per million hours). Function-flows with the highest and lowest failure rates were both actuate electrical energy and import human energy (25.81 failures per million hours) and import electrical energy (0.0021 failures per million hours). Bo#le&Capping&Machine& Reliability% 76.1%% 61.1%% 48.8%% 7.1%% CFG% Maximum% Average% Minimum% FIGURE 7: Reliability Results for the Bottle Capping Machine Eleven components and twelve functions were excluded from the reliability calculations. This was due to either the function-flow or component not having failure rate data. In either case, the components and function-flows were mapped to each other and both were excluded. Without being able to account for the data in a design, uncertainty is introduced to the calculation. This is a limitation to the choice of using the functionflow failure rates in the proposed methodology. The three products evaluated were not chosen because they had failure rate data, as this would not be the case in a design project. They were chosen because they had complete CFG and FM which were already generated. 22 In the three designs evaluated, two function-flows resulted in two components that ultimately lowered the system level reliability. These functions include export solid, and converts electrical energy to rotational mechanical energy, and their corresponding components were brush, and electric motor. In the toothbrush, the two brush components had a combined series failure rate of 18.30 failures per million hours while their corresponding function-flows had a combined failure rate of 56.92 failures per million hours. The brushes individually had the second highest failure rate in the product and account for approximately half of the failures that would occur in the toothbrush. Similarly, their corresponding functionflows make up for half of the failures in the weighted average. For the automated bottle capping machine, the component with the highest failure rate, an electric motor, was present twice in the design. The combined series failure rate of these motors is 18.48 failures per million hours. In this design, the electric motor converts electric energy to rotational mechanical energy. This function occurs twice in the functional model and has a combined failure rate of 18.77 failures per million hours. The two electric motors account for approximately 40% of the overall failure rate while the conversion from electrical to rotational energy accounts for approximately 25% of the combined failure rate using the proposed methodology. This information shows that critical components can be identified using the proposed methodology. The comparison between these shows a positive result for the use of the proposed data. Understanding the range for the reliability before any components have been selected is a useful tool in the early design stage. 5. CONCLUSION The effort to move reliability engineering into the early stage of design is an increasing area of interest. This research aims to increase knowledge of the system at the functional level. Currently, failure rate data is available for components. Here similar data has been generated for function-flows to give designers the same advantage at the functional level of design. This was done using a FCM and the Heaviside function. 23 The Heaviside function required that function-flows were solved with enough occurrences to be counted which protects them from inheriting failure rate data from components that are rarely their solution. The new failure rate data has been used to make decisions at the design phase and determine system reliability with a weighted average and an upper and lower bound. This was done using the proposed methodology. 6. FUTURE WORK The component failure rate data used from NPRD-95 does not give any indication of how a component failed. As discussed previously, a failure observed in this document was described as solving the symptoms of failure. Research has been done to break function failures into failure modes based on a set number of failures. This method will be examined to find a way to get a failure rate of a failure mode for a specific function-flow. This data provides the designer more information in the early design stage and will help guide important design decisions 7. ACKNOWLEDGMENTS This research was funded in part by DARPA (Subaward to FA8650-10-C-7079 with Palo Alto Research Center). The opinions, findings, conclusions, and recommendations expressed are those of the authors and do not necessarily reflect the views of the sponsors. 24 APPENDIX A: Function-flow Failure Rates Function-flow Wtd Avg Min Max Function-flow Fails/Mhours Fails/Mhours Fails/Mhours actuate control actuate control to electrical actuate electrical actuate human energy actuate human material actuate mechanical actuate solid-liquid change control change electrical change electromagnetic change hydraulic change liquid change material change mechanical change rotational change signal change solid change solid-liquid change translational collect gas-gas condition control condition electrical convert chemical to mechanical convert chemical to thermal convert control to status convert electrical convert electrical to electromagnetic convert electrical to mechanical convert electrical to optical convert electrical to rotational convert electrical to status convert electrical to thermal convert electromagnetic to electrical convert electromagnetic to mechanical convert gas to liquid convert human energy to control convert human energy to mechanical convert human energy to rotational convert human material to control convert human material to mechanical convert liquid to colloidal convert liquid to gas convert magnetic to control convert magnetic to mechanical convert mechanical convert mechanical to acoustic convert mechanical to electrical convert mechanical to hydraulic convert mechanical to pneumatic convert mechanical to rotational convert mechanical to status convert mechanical to thermal convert pneumatic to mechanical convert pneumatic to rotational convert pneumatic to translational convert rotational to pneumatic convert rotational to translational convert solid to liquid convert translational to rotational couple electrical couple solid 1.97E+0 8.20E-1 1.25E+0 1.79E-1 1.79E-1 7.25E+0 5.84E+0 4.59E+0 2.01E+0 7.48E+0 3.93E-1 7.18E+2 1.23E+2 5.11E+0 4.56E+0 1.92E+2 1.45E+2 2.00E-2 6.20E+0 3.61E+0 1.83E+0 1.83E+0 6.63E+0 3.99E+2 1.57E+1 2.34E+0 6.72E+0 9.24E+0 1.81E+0 9.39E+0 5.73E-1 4.04E-1 7.41E+0 2.21E-2 2.53E+1 2.01E+0 5.26E+0 3.81E+0 8.20E-1 2.21E-2 1.20E+1 4.06E+0 3.61E+0 2.21E-2 9.26E+0 8.31E+0 2.02E+2 2.88E+1 1.14E+1 2.92E+0 5.28E-1 2.68E+2 2.00E-1 2.00E-1 7.83E+0 1.20E+1 9.05E+0 1.20E+1 1.11E+1 4.59E+0 9.71E+0 8.20E-1 8.20E-1 1.79E-1 1.79E-1 1.79E-1 1.79E-1 5.47E+0 4.59E+0 9.00E-2 2.21E-2 3.93E-1 7.18E+2 5.40E+1 9.30E-1 2.92E+0 1.92E+2 2.00E-2 2.00E-2 6.20E+0 3.61E+0 1.83E+0 1.83E+0 6.63E+0 6.63E+0 5.73E-1 9.00E-2 1.62E-1 5.00E-1 5.73E-1 9.24E+0 5.73E-1 2.00E-2 3.61E+0 2.21E-2 8.08E+0 1.79E-1 1.79E-1 3.81E+0 8.20E-1 2.21E-2 1.20E+1 2.00E-2 3.61E+0 2.21E-2 3.72E+0 6.63E+0 3.61E+0 1.20E+1 2.00E-1 2.92E+0 5.28E-1 6.63E+0 2.00E-1 2.00E-1 2.00E-1 1.20E+1 1.95E-1 1.20E+1 3.88E+0 4.59E+0 1.80E-3 2.58E+1 8.20E-1 2.58E+1 1.79E-1 1.79E-1 2.58E+1 6.20E+0 4.59E+0 4.59E+0 1.12E+1 3.93E-1 7.18E+2 1.92E+2 1.97E+1 4.69E+0 1.92E+2 7.18E+2 2.00E-2 6.20E+0 3.61E+0 1.83E+0 1.83E+0 6.63E+0 5.30E+2 3.60E+1 4.59E+0 4.48E+1 2.58E+1 3.04E+0 1.20E+1 5.73E-1 8.08E+0 1.12E+1 2.21E-2 3.39E+1 1.34E+1 2.58E+1 3.81E+0 8.20E-1 2.21E-2 1.20E+1 8.08E+0 3.61E+0 2.21E-2 1.55E+1 9.15E+0 5.30E+2 4.57E+1 3.60E+1 2.92E+0 5.28E-1 5.30E+2 2.00E-1 2.00E-1 1.55E+1 1.20E+1 1.97E+1 1.20E+1 1.97E+1 4.59E+0 7.18E+2 Wtd Avg Min Max Fails/Mhours Fails/Mhours Fails/Mhours display status distribute electrical distribute liquid distribute material distribute mechanical distribute optical distribute solid distribute thermal export acoustic export control export electrical export electromagnetic export gas export human energy export human material export hydraulic export liquid export liquid to colloidal export mechanical export mixture export optical export pneumatic export rotational export rotational to translational export signal export solid export solid-liquid export status export thermal export translational guide electrical guide gas guide human energy guide human material guide hydraulic guide liquid guide mechanical guide mixture guide pneumatic guide radioactive/nuclear guide rotational guide signal guide solid guide solid-gas guide solid-liquid guide thermal guide translational import chemical import control import electrical import gas import human energy import human material import hydraulic import liquid import mechanical import mixture import optical import pneumatic import rotational import solid 5.40E+1 4.30E+0 2.41E+2 3.64E+2 8.89E+0 5.73E-1 7.18E+2 6.43E+0 6.63E+0 2.10E-3 1.84E+0 2.27E+1 1.17E+2 1.79E-1 3.12E+0 6.84E+0 2.67E+1 2.25E+0 5.29E+0 6.44E+0 6.31E+0 1.54E+2 3.71E+0 2.25E+0 3.61E+0 1.21E+1 7.18E+2 3.14E+1 4.49E+0 1.97E+1 2.38E+0 1.34E+2 1.10E+1 3.45E+0 6.07E+0 7.95E+0 5.84E+0 2.43E+2 7.45E+0 1.12E+1 5.73E+0 2.08E+1 6.17E+0 7.18E+2 5.47E+0 1.82E+2 9.95E+0 3.62E+2 1.84E+0 2.98E+0 2.22E+2 2.70E+0 2.63E+0 2.93E+0 2.38E+1 3.96E+0 9.15E+0 1.12E+1 1.88E+2 4.01E+0 7.93E+0 5.40E+1 5.28E-1 2.92E+0 9.15E+0 1.95E-1 5.73E-1 7.18E+2 6.12E-2 6.63E+0 2.10E-3 1.90E-2 5.73E-1 2.25E+0 1.79E-1 1.31E-2 1.95E-1 9.00E-2 2.25E+0 2.10E-3 5.28E-1 3.04E+0 8.08E+0 1.95E-1 2.25E+0 3.61E+0 2.00E-2 7.18E+2 5.73E-1 2.00E-2 1.97E+1 2.33E+0 2.27E+0 1.10E+1 1.31E-2 1.95E-1 9.00E-2 5.28E-1 5.28E-1 6.20E+0 1.12E+1 1.95E-1 2.08E+1 1.80E-3 7.18E+2 5.47E+0 8.08E+0 1.95E-1 6.63E+0 1.79E-1 2.10E-3 2.00E-1 1.31E-2 1.31E-2 1.95E-1 2.00E-2 2.10E-3 9.15E+0 1.12E+1 6.20E+0 1.95E-1 1.80E-3 5.40E+1 8.08E+0 7.18E+2 7.18E+2 2.08E+1 5.73E-1 7.18E+2 1.97E+1 6.63E+0 2.10E-3 3.61E+0 4.48E+1 7.18E+2 1.79E-1 1.97E+1 1.34E+1 7.18E+2 2.25E+0 2.58E+1 9.15E+0 1.12E+1 7.18E+2 9.63E+0 2.25E+0 3.61E+0 7.18E+2 7.18E+2 5.40E+1 1.97E+1 1.97E+1 2.50E+0 7.18E+2 1.10E+1 1.10E+1 1.34E+1 3.60E+1 1.97E+1 7.18E+2 8.08E+0 1.12E+1 1.97E+1 2.08E+1 7.18E+2 7.18E+2 5.47E+0 5.30E+2 1.97E+1 7.18E+2 1.12E+1 1.10E+1 7.18E+2 2.58E+1 1.97E+1 8.08E+0 7.18E+2 1.97E+1 9.15E+0 1.12E+1 7.18E+2 1.97E+1 7.18E+2 25 APPENDIX A (continued): Function-flow Failure Rates Function-flow Wtd Avg Min Max Function-flow Fails/Mhours Fails/Mhours Fails/Mhours import solid-liquid import thermal import translational indicate control indicate electromagnetic indicate signal indicate status indicate visual join solid link solid position human material position liquid position mechanical position solid process control process electrical process status regulate control regulate electrical regulate gas regulate hydraulic regulate liquid regulate material regulate mechanical regulate pneumatic regulate solid regulate thermal secure human material secure mixture secure solid secure solid-liquid sense control sense electrical sense solid sense status sense thermal separate gas separate material separate mixture separate solid shape solid stabilize mechanical stop electrical stop gas stop hydraulic stop liquid 2.94E+1 5.31E+0 9.63E+0 5.73E-1 1.89E+1 1.02E+0 1.34E+1 5.40E+1 4.92E+0 2.92E+0 1.25E+1 1.15E+1 3.61E+0 3.81E+0 4.59E+0 3.61E+0 5.73E-1 2.36E+0 3.13E+0 9.55E+1 4.18E+0 5.73E+0 3.01E+1 4.00E+0 5.47E+0 9.73E+1 1.33E+1 1.97E+1 9.15E+0 5.52E+0 1.92E+2 4.10E+0 1.32E+1 4.98E+1 2.04E+1 8.45E+0 1.92E+2 9.63E+1 6.20E+0 6.65E+0 5.40E+1 3.61E+0 1.28E+0 4.45E+1 5.47E+0 5.39E+0 2.27E+0 6.12E-2 9.63E+0 5.73E-1 5.73E-1 1.62E-1 1.79E-1 5.40E+1 1.95E-1 2.92E+0 1.10E+1 9.63E+0 3.61E+0 1.80E-3 4.59E+0 3.61E+0 5.73E-1 8.20E-1 9.00E-2 5.47E+0 4.23E-1 4.23E-1 6.20E+0 1.80E-3 5.47E+0 4.57E+1 1.33E+1 1.97E+1 9.15E+0 1.80E-3 1.92E+2 3.61E+0 1.32E+1 4.57E+1 3.61E+0 3.61E+0 1.92E+2 5.00E-1 6.20E+0 4.23E-1 5.40E+1 3.61E+0 6.12E-2 5.47E+0 5.47E+0 2.00E-2 1.92E+2 1.97E+1 9.63E+0 5.73E-1 4.48E+1 3.61E+0 5.40E+1 5.40E+1 2.08E+1 2.92E+0 1.97E+1 1.34E+1 3.61E+0 7.18E+2 4.59E+0 3.61E+0 5.73E-1 6.20E+0 2.58E+1 5.30E+2 1.34E+1 1.34E+1 5.40E+1 4.69E+0 5.47E+0 1.92E+2 1.33E+1 1.97E+1 9.15E+0 7.18E+2 1.92E+2 4.59E+0 1.32E+1 5.40E+1 5.40E+1 1.33E+1 1.92E+2 1.92E+2 6.20E+0 9.15E+0 5.40E+1 3.61E+0 2.50E+0 1.92E+2 5.47E+0 1.34E+1 Wtd Avg Min Max Fails/Mhours Fails/Mhours Fails/Mhours stop liquid to colloidal stop material stop mixture stop pneumatic stop rotational to translational stop solid stop thermal store chemical store control store electrical store gas store hydraulic store liquid store mechanical store mixture store pneumatic store solid store solid-liquid supply electrical supply gas supply hydraulic supply liquid supply mechanical support solid transfer chemical transfer control transfer electrical transfer gas transfer human energy transfer hydraulic transfer liquid transfer mechanical transfer rotational transfer signal transfer solid-liquid transfer status transfer thermal transmit control transmit electrical transmit human energy transmit mechanical transmit pneumatic transmit rotational transmit thermal transport solid 2.25E+0 5.40E+1 5.47E+0 5.47E+0 2.25E+0 4.60E+0 2.05E+0 4.08E+0 4.59E+0 4.10E+0 1.92E+2 2.00E-1 3.13E+0 1.52E+0 2.25E+0 6.20E+0 3.87E+0 2.25E+0 3.94E+0 1.92E+2 2.00E-1 3.33E+0 1.16E+0 1.46E+0 7.18E+2 4.19E+0 3.42E+0 1.56E+1 9.87E+0 6.08E+0 2.66E+2 6.93E+0 3.97E+0 1.79E-1 2.49E+2 3.61E+0 4.15E+0 5.40E+1 1.41E+1 1.02E+1 7.86E+0 2.08E+1 4.91E+0 6.63E+0 1.47E+1 2.25E+0 5.40E+1 5.47E+0 5.47E+0 2.25E+0 1.95E-1 6.12E-2 4.08E+0 4.59E+0 4.08E+0 1.92E+2 2.00E-1 2.25E+0 1.95E-1 2.25E+0 6.20E+0 2.25E+0 2.25E+0 2.33E+0 1.92E+2 2.00E-1 2.25E+0 1.95E-1 1.80E-3 7.18E+2 1.80E-3 2.10E-3 1.20E+1 1.83E+0 2.00E-1 3.39E+1 1.80E-3 9.30E-1 1.79E-1 1.95E-1 3.61E+0 1.90E-2 5.40E+1 1.90E-2 1.83E+0 3.81E+0 2.08E+1 1.95E-1 2.00E-2 9.63E+0 2.25E+0 5.40E+1 5.47E+0 5.47E+0 2.25E+0 5.40E+1 2.25E+0 4.08E+0 4.59E+0 4.59E+0 1.92E+2 2.00E-1 1.20E+1 1.97E+1 2.25E+0 6.20E+0 1.20E+1 2.25E+0 4.59E+0 1.92E+2 2.00E-1 1.20E+1 3.81E+0 2.92E+0 7.18E+2 1.33E+1 9.24E+0 3.39E+1 1.10E+1 1.20E+1 7.18E+2 7.18E+2 1.97E+1 1.79E-1 7.18E+2 3.61E+0 1.97E+1 5.40E+1 5.40E+1 1.97E+1 2.08E+1 2.08E+1 9.63E+0 1.97E+1 1.97E+1 26 Link Between Function-Flow Failure Rates and Failure Modes for Early Design Stage Reliability Analysis Authors Bryan M. O’Halloran 100 Dearborn Hall Email: ohallorb@onid.orst.edu Robert B. Stone Ph.D 406 Rogers Hall Email: rob.stone@oregonstate.edu Irem Y. Tumer Ph.D 408 Rogers Hall Email: irem.tumer@oregonstate.edu Proceedings of the 2011 ASME International Mechanical Engineering Congress and Exposition Safety Engineering, Risk Analysis, and Reliability Methods IMECE 2011 November 11-17, 2011, Denver, CO, United States of America 27 ABSTRACT The scope of this paper is to provide an extension to the Function Failure Design Method (FFDM). We first implement a more robust knowledge base using Failure Mode/Mechanism Distributions 1997 (FMD-97). Then failure rates from Nonelectric Parts Reliability Data (NPRD-95) are added to more effectively determine the likelihood that a failure mode will occur. The proposed Functional Failure Rate Design Method (FFRDM) uses functional inputs to effectively offer recommendations to mitigate failure modes that have a high likelihood of occurrence. This work uses a past example where FFDM and Failure Modes and Effects Analysis (FMEA) were compared to show that improvements have been made. A four step process is presented to show how the FFRDM is used during conceptual design. 1. INTRODUCTION In the process of design, functionality is where the voice of the customer is captured. For this reason, failure can be defined as the loss of functionality [1]. Meaning that if the design stops working in the way the customer prefers, it has failed. Since we design for functionality, data in this research has been tabulated to provide designers the capability to perform accurate reliability analyses directly after generating a functional model. Functional modeling is performed at the conceptual stage of design before any components have been determined [2]. This data has been carefully calculated using historical failure information and relationships between functions and components. Although, here the failure rates are linked to specific failure modes and offer the likelihood that the failure mode will occur given that a specific function-flow appears in the functional model. Performing reliability analysis at the conceptual level of design offers the power of risk informed decision making to the designer. As the design process continues it becomes increasingly expensive to make design changes. Providing an analysis that can mitigate this problem at the conceptual level may significantly reduce the likelihood of costly failure events. 28 2. BACKGROUND This section provides a survey of the relevant related research. These topics include Functional Modeling, FFDM, Risk in Early Design, and Failure Rates, Modes, and Mechanisms. 2.1. Functional Modeling Functional modeling is a standard part of many engineering design methodologies and is used to describe a design at an abstract level. Generating a functional model is done early in the design process before components have been chosen in an original design problem or before reviewing existing component choices in a redesign problem. The design process, in a general sense, follows five steps; project definition and planning, specification definition, conceptual design, product development, and product support [26]. The functional design method is used in the first stage of conceptual design. The format of functional models consists of functions connected by flows. The three types of flow include material, energy, and signal. Stone [27] standardized functional modeling by creating a common functional basis which provided a set number of functions and flows to describe the entire design space. The functional basis provides consistency across functional models of different designs. The functional basis is used as the starting point for this research. Failure rates of failure modes are found here for each term in the functional basis. Appendix A presents this data in a summarized version due to page limit restrictions. This includes each functional basis term. Table 1 gives an example using nail clippers for how the Functional Basis is different from describing a design using general functionality. 29 TABLE 1: Example Using Functional Basis Terminology General - Accept user’s hand - Position user’s hand - Move clipper to desired location - Apply force on lever to actuate clipper - Return clippers to storage - Release user’s hand 2.2. Functional Basis - Import Human Energy - Import Human Material - Import Solid Material - Guide Solid Material - Position Solid Material - Actuate Solid Material - Guide Solid Material - Position Solid Material - Export Human Energy - Export Human Material - Export Solid Material Function Failure Design Methodology FFDM is a structured formulation of the function-failure analysis method introduced by Tumer and Stone [3], and is used to perform failure analysis in the conceptual design stage. This method also aids the designer by using a function-based concept generator approach which helps streamline the design process [20]. The proposed extension to FFDM, FFRDM, does not use this concept generation. Instead, FFRDM is used only to inform the designer at the functional level of design. FFDM utilizes knowledge bases which link product function to failure modes. The knowledge base data is archived in the form of a function-component matrix and a componentfailure mode matrix. This reduces the need for a designer to have a large intellectual knowledge base. FFDM has several advantages including reduced high user workload, using an archived failure knowledge base, being usable during functional design, using the functional basis, component taxonomy, and failure mode taxonomy as a formalized failure language, and is practical for electrical and mechanical systems [21]. Currently, FFDM lacks a strong component failure mode knowledge base. Only 63 failure mode occurrences have been observed in this framework previously [3]. Adding to the knowledge base provides confidence in the results. Using FMD-97 [28], this research has added approximately 36,700 failure mode occurrences to the component-failure mode matrix. 30 2.3. Risk in Early Design Risk in Early Design (RED) is a conceptual design tool which uses functional inputs to assess risk. An algorithm along with historical failure data is combine to provide the designer failure modes, likelihood, and severity from the functional inputs. The RED database is populated by three sources including functional models, bill of materials, and failure reports. Bill of materials and failure reports provide the component name and failure mode occurrence respectively. Data is converted using naming taxonomies for failure modes [29], components [30], and functions [27] to standardize the process. Each taxonomy is explicitly defined and defines the entire set of potential names. Figure 1 shows how each source correlates to matrices EC, CF, and EF. The matrix EF is produced by multiplying matrix EC by CF. FIGURE 1: Red Database Population This information can be used to determine the respective difference in occurrence between failure modes for a specific function. Similarly it can be determined which failure modes globally occurs with the greatest frequency. Although, this can not be used to predict likelihood of a failure mode. The current CF 31 matrix has approximately 600 observed occurrences. The proposed method has observed over 36,700 occurrences to provide more robust results. Using sixty times the number of occurrences will give the designer confidence that the method is well backed by a large knowledge base. In addition to this calculation, RED provides calculations for failure severity and likelihood. Failure severity was gathered through studying NASA, FMEA, and risk engineering sources. These sources provide the foundation to generate the CF’ matrix using scores from 0 to 5, where 5 is the most severe. A similar matrix calculation was performed as in Figure 1. The result is the occurrence of functional failure severity. Failure likelihood was generated from a detailed list of component failure occurrences. The failures were sorted low to high based on their occurrences. These were also categorized in to a 0 to 5 scale and a matrix calculation was performed to determine the likelihood of the functional failures. The likelihood data was tabulated solely using failure occurrence. Likelihood cannot be determined in the absence of time since failure is time dependent. While strictly using occurrence data, common components will observe increased likelihood because they are used more often. Less common components, which may have a higher failure rate, could receive a lower likelihood value because their failures are observed less often. The solution is to use failure rate information in the place of recorded failure occurrence. The FFRDM knowledge base proposed in this research provides failure rates of failure modes for specific functions. This is the necessary data to generate quantitative likelihood results at the conceptual stage of design. 2.4. Failure Rates, Modes, and Mechanisms Failure rate (λ) is a commonly used and well accepted variable found during risk and reliability calculations. In general, (λ) is recorded in units of Failure/Million Hours or Failure/Million Miles. This depends on the source and how the data was collected. A common problem in reliability engineering is how failures can be mitigated. The root of this problem can be better understood by the cause and result of a failure. 32 Depending on the source, the terms failure mode and failure mechanism are defined differently. Often, they are used interchangeably as the end state of a failure. Collins uses the term failure mode as the physical process or processes that produce a failure [31]. Blischke and Murthy define this as the description of a fault. Although, neither provide a definition for failure mechanism. FMD-97 defines failure mode as the observable consequence of failure. Here, this definition is adopted and is extended to also include any change in behavior. FMD-97 defines failure mechanism as the physical process which causes the failure. This definition will also be adopted. A common vocabulary of failure modes has been developed for mechanical systems by Collins [31]. Work done by Stone and Tumer [29] has provided a failure mode taxonomy for both electrical and mechanical systems. The latter will be used here to convert failure modes from those listed in FMD-97. Although, for mechanical failure modes that appeared in both taxonomies, definitions/descriptions were consulted from Collins text to gather more consensus. 2.5. Failure Modes and Effects Analysis The goal of FMEA is to identify, evaluate, and prevent critical component or functional failures [5]. FMEA can be performed in exactly the same manner using either components or functions. Failure is commonly defined as a loss in functionality and therefore this research focuses on FMEA using functions. Critical functions receive a recommended schedule and action to reduce the failure mode risk. FMEA is a tool used to analyze systems to gather information that a decision can be made from. High risk functions are determined by the risk priority number (RPN). The FMEA analysis starts by identifying a list of functions and their potential failure modes. A list of functions can be produced from the functional model while a list of components is produced from the detailed component design architecture. Failure modes are determined by expert knowledge or extensive research of similar designs. The RPN value is the product of three variables; occurrence, severity, and likelihood of detection. Occurrence refers to the likelihood that the failure will occur, severity is how bad the failure is, and likelihood of detection is how hard the failure is to detect. 33 From the list of potential failures, the occurrence, severity, and likelihood of detection are scored on a scale of 1 to 10, resulting in an RPN value in the range of 0 to 1000. The usefulness of FMEA as a design tool is to look at the RPN values relative to each other and determine which functions need action taken and which do not. From this analysis, the designer can determine the critical functions of a system and make design changes accordingly. Information for single failure mode input into the FMEA is not a long process. This simply involves entering the function, an associated failure mode, then listing the severity, detection, and occurrence values. These values are also subjective and can lead to a poor analysis of critical failures. Although, to perform a complete FMEA for the entire design can be very time consuming. This involves generating a list of potential failure modes for each function. At a functional level this is not intuitive and at a component level would require domain-specific expert knowledge. Some functions, or components, can have over 50 distinct failure modes that should be considered. Next, each failure mode must have the severity, detection, and occurrence determined and recorded. Once this is done, it must be determined which functions have too high of an RPN value, then recommended actions must be recorded. In all, this analysis becomes very time consuming. FMEA also requires expert engineers to properly perform. Experts have acquired a knowledge base that only they have access to. Although, even the seasoned professional can miss failure modes with high occurrences. Using a computerized knowledge base solves this simple mistake. Experts have recorded data for years which has been grouped in to a single data source. The data found in this research was calculated using this historical failure rate data. Engineers with little experience in a specific field can use this data to produce expert level results. The research described in this paper provides a solution to FMEA. This can reduce the time required by an expert, or in some cases, eliminate the need for an expert altogether. In FFRDM the functional model is used to generate the relevant failure modes for a design. Failure modes are provided with failure rates as a way to accurately determine the occurrence. Calculating the RPN value is not needed. Prior 34 work has shown that final recommendations by FFDM can exceed those of FMEA [3]. This example is revisited to show that improvements have been made in the extension from FFDM by providing further useful recommendation and discussing recommendations given previously that had low occurrence values. 3. RESEARCH APPROACH This section provides information and the steps followed to arrive at the knowledge base for FFRDM. Two data sources were used as a starting point, NPRD-95 and FMD-97. Failure modes in FMD-97 were converted to a failure mode taxonomy. A repository of product information was used to generate function to component relationships. These relationships in conjunction with NPRD-95 and FMD-97 were used to build the knowledge base for FFRDM. 3.1. Component Failure Rate Data Source [32] NPRD-95 was used as the source of the component failure rate data. NPRD-95 was put together by Reliability Information Analysis Center. This reference is an ongoing effort to collect and provide high volumes of data from a variety of sources including both military and commercial. This specifically includes warranty manuals, government sponsored studies, published papers and reports, databases, and military maintenance systems. From the previous publication, NPRD-91, 56% more data has been acquired. A strong emphasis was put on data quality during the collection phase. This was done by ensuring completeness of data, consistency of data, equipment population tracking, failure verification, and characterization of operation histories. Often data is discarded if it does not meet quality standards. This document did not indicate failure modes or mechanisms. Failure, as observed in NPRD-95, is classified generically under solving the symptoms of the failure. A part failed if, when it was replaced, the failure symptoms were not present anymore. Comprehensive indices are provided for background on the parts and sampling. These include the component manufacturer, model or part number, nominal performance specifications specific to each part, population tested, number of 35 operation hours, and number failed. The operating hours and number of parts failed is used to generate failure rates for both specific components and component classes. For example, a failure rate is provided for a specific type of actuator, then a combined failure rate is given for the actuator class. The failure rate for each component class is the sum of the total components failed for that class divided by the sum of the operating hours for each component in that class. Calculating both types of data lets the user employ the data at a generic or specific level. This data was employed in the Component-failure mode matrix. A component naming taxonomy was used to define the entire set of components that would be used in both the function-component and component-failure mode matrix. This taxonomy was also used to look up values in NPRD-95. For each component in the taxonomy that also appeared in NPRD-95, a failure rate was recorded. For components that did not match verbatim, definitions in the component naming taxonomy were used to determine whether or not a failure rate value should be recorded. 3.2. Failure Modes and Mechanism Data Source [28] FMD-97 is a document constructed by the Reliability Information Analysis Center to provide high volumes of data on failure modes and mechanisms. This data is collected from a variety of sources and presented in a single document. Failure modes and mechanisms are given for electrical, electronic, mechanical, and electromechanical parts and assemblies. FMD-97 is the second edition of this document replacing FMD-91. Important improvements have been made including a new algorithm used to combine data sources and additional raw data that has been collected since the first edition was published. These have significantly improved the quality of this document and the usability of the data. The data in FMD-97 was used to populate the component-failure mode matrix. In the same manner as the component naming taxonomy, failure modes in this document were fit to a failure mode taxonomy [29]. Definitions provided in the 36 taxonomy were used for justification when names were not verbatim. Also, the data details section of FMD-97 offered additional information for this justification. Four failure mode categories were created to accommodate those failure modes which did not adequately fit to the taxonomy. These include control issue, unknown, other, and artifact failure. A control issue is the loss in control or communication of the design, but also includes signal losses. This does not indicate any sort of physical failure necessarily. This could in many cases, for example, be a software failure. In a sensor, this would be the inability to retrieve data stored on the sensor even though it exists. Intermittent operation is also included here. The unknown category was listed within FMD-97. Failures were recorded, but the cause and result was not. For obvious reasons, this data could not be converted to anything listed in the failure mode taxonomy and was therefore left as unknown. The other category was also a category listed in FMD-97 and was reserved for failure modes which are rarely observed for a component type. Although the occurrence of the other is high (see Appendix A for data), the occurrence within this category for any given failure mode is very low. For this reason the data within the other category in FMD-97 was added up and kept under the listing other. As described previously, failure modes and failure mechanisms are defined differently in this research. FMD-97 provides both but does not distinguish between the two within the data, even though the cause and result of a failure are significantly different phenomenon in many cases. The category artifact failure was created to parse out what were considered to be the cause of the failure. There does not currently exist a failure mechanism taxonomy used for design. Parsing these out was done by proving which were failure mechanisms. Any failure mode/mechanism listing in FMD-97 with an artifact in it was added to the artifact failure category. When FMD-97 lists these failure modes/mechanisms under a component, the assumption is that the listed artifact was the cause and not the result. For example, the component connector has failed 8 times by a contact failing and 4 by wire fracturing. Both contact and wire are artifacts of the component connector and were recorded as failure mechanisms. Both Design and Workmanship were also grouped with artifact failure since their 37 names describes them as predating the failure. Listings with specific information such as loss of capacitance or change in resistance are included as failure modes because they imply a specific change in behavior. Those such as electrical failure and excessive leakage are more general and were also defined as failure modes. 3.3. Repository Data The Design Engineering Lab Repository (http://designengineeringlab.org/ delabsite/repository.html) at Oregon State University was used for function component mapping and data structuring. A function-component matrix was queried from the repository using terms from the functional basis and component naming taxonomy [29]. The function-component matrix is used to capture the relationship between the functions and component naming terms. The function-component matrix lists component naming terms across the first row as column headers and function-flow pairs down the first column. The matrix is then filled with the occurrences of the number of times a function is solved by a component. The matrix is populated in a column format where every occurrence is listed for a specific component before any are listed for the next component. This is because functions are related to components in the repository database and not the other way around. There are 164 components from the component naming terms listed and 731 function-flows. The total number of occurrences is 16,365. 38 Function(Component-Matrix Failures/Mhours 192.0795 x 0.1949 2.2727 15.4501 0.1624 x x Generated-On:-Wed-Jan-26-22:44:46-PST-2011 converter conveyer coupler cover crank digital-display diode distributor convert-pneumatic-to-status 0 0 0 0 0 0 0 1 convert-pneumatic-to-translational 0 0 0 0 1 0 0 0 convert-radioactive/nuclear-to-chemical 0 0 0 0 0 0 0 0 convert-radioactive/nuclear-to-control 0 0 0 0 0 0 0 0 convert-radioactive/nuclear-to-electrical 0 0 0 0 0 0 0 0 convert-rotational-to-acoustic 0 0 0 0 0 0 0 0 convert-rotational-to-electrical 0 0 0 0 0 0 0 0 convert-rotational-to-hydraulic 0 0 0 0 0 0 0 0 convert-rotational-to-mechanical 0 0 0 0 0 0 0 0 convert-rotational-to-pneumatic 0 0 0 0 0 0 0 0 convert-rotational 0 0 0 0 0 0 0 0 convert-rotational-to-status 0 0 0 1 0 0 0 0 convert-rotational-to-translational 0 0 2 0 0 0 0 0 convert-signal-to-status 0 0 0 0 0 0 0 0 convert-signal-to-visual 0 0 0 0 0 1 0 0 convert-solar-to-chemical 0 0 0 0 0 0 0 0 convert-solar-to-electrical 2 0 0 0 0 0 0 0 convert-solar-to-status 0 0 0 0 0 0 0 0 convert-solar-to-thermal 1 0 0 0 0 0 0 0 convert-solid-to-chemical 0 0 0 0 0 0 0 0 convert-solid-to-liquid 0 0 0 0 0 0 0 0 convert-solid 1 0 0 0 0 0 0 0 convert-solid-to-solid(solid 0 0 0 0 0 0 0 0 convert-status-to-analog 0 0 0 0 0 0 0 0 convert-status-to-control 0 0 0 1 0 0 0 0 convert-status-to-electrical 0 0 0 0 0 0 0 0 FIGURE 2: Function-Component Matrix Snippet The example function-component matrix snippet in Figure 2 shows convert rotational to translational being solved twice by the coupler. Zeros in the matrix indicate that there is no observed relationship in the repository of the particular function-flow and component. The component naming terms along the first row of the function-component matrix are specifically defined [24]. These terms line up with the component classes listed in NPRD-95. 3.4. Converging Data Using Matrix Multiplication Two matrices, discussed in section 3.1 through 3.3, were generated to create the FFRDM knowledge base. Once the component-failure mode matrix was populated with occurrences of the failure modes, each row was normalized. The failure rates, recorded from NPRD-95 for each component, were listed adjacent to each component name. Each cell containing the normalized failure mode occurrence was multiplied by the component failure rate. This distributed the failure rate of a component between all of its observed failure modes. The result of this calculation is the failure rate of a failure mode for a specific component. 39 The next step was done by multiplying the function-component matrix by the component-failure mode matrix. The function-component matrix is 731 cells by 165 cells and the component-failure mode matrix is 165 cells by 39 cells. As a result of the large sized matrices, the matrix multiplication was carried out in Matlab. The results were then exported back in to excel. The result of this calculation is the failure rate of a failure mode for a specific function and therefore the knowledge base for FFRDM. 4. RESULTS This section begins with a description of the FFRDM knowledge base. FFRDM during the design process is then described using four steps. An example is used to show how this process takes place. Recommendations are provided for this example based on a functional model and the likelihood of occurrence. 4.1. Failure Mode Data In Appendix A, the FFRDM knowledge base is presented in a table format. Due to size restriction, data is presented for functions instead of function-flows. Figure 3 shows a snippet of the full data set. The top row are failure modes taken from the failure modes taxonomy and the first column are function-flows from the functional basis. The cells in the matrix are failure rates in failures per million hours. These values represent the number of times a function-flow will fail in a specific failure mode for every million hours of operation. Values of zero indicate that there does not exist a relationship between a failure mode and function flow. It should be noted that this work does not claim that functions have failure modes. Rather, this research has found that functions are linked to components which have failure modes. The function-component and component-failure mode relationships prove that a relationship does exist between functions and failure modes. Although, it does not make sense to say that the failure mode belongs to the function since it was observed from a component failing. 40 !"#$%&'#()*'+,!-&*./01'2/ $'..'3&'# $.-$4&#5 /96'.%0/*/$%.'7-5#/%&$ :;:::< : /96'.%05-3 :;:=:> :;::<? /96'.%05-3(5-3 : : /96'.%08"7-#0/#/.5B :;::=? :;:::@ /96'.%08"7-#07-%/.&-* :;::<A :;:=>D /96'.%08B2.-"*&$ :;::@E :;::== /96'.%0*&F"&20%'0$'**'&2-* : : /96'.%0*&F"&2 :;:=C? :;::>@ /96'.%0*&F"&2(5-3 :;::> :;:::< /96'.%0*&F"&2(*&F"&2 : : /96'.%07-5#/%&$ : : /96'.%07/$8-#&$-* :;:<<? :;:=@? /96'.%07&9%"./ : :;:=CA /96'.%0'6%&$-* :;:::< :;:==A /96'.%06#/"7-%&$ :;::D :;::=< /96'.%0.-2&'-$%&G/,#"$*/-. : :;:==< /96'.%0.'%-%&'#-* :;::C? :;:::? /96'.%0.'%-%&'#-*0%'0%.-#3*-%&'#-* : : /96'.%03&5#-* : : /96'.%03'*&2 :;:<A :;:A=@ /96'.%03'*&2(*&F"&2 : : /96'.%03%-%"3 :;::@? :;::== /96'.%0%8/.7-* :;:=:@ :;::>? /96'.%0%.-#3*-%&'#-*0%'0-$'"3%&$ : : /96'.%0%.-#3*-%&'#-* :;:::= :;:::= $.//6 : :;::=@ : :;::=C :;:<@> :;:::> : :;::@> : : : :;:> :;:AEE : :;:::A : :;::=A : : :;:E<C : :;:<<< :;::@ : :;:::? )-%&5"/ : : : :;:::= :;:<=< : : :;::=A : : : :;:::A : : : : :;:::> : : :;::<A : :;:::= : : : )./%%&#5 : :;:::= : :;:::> :;:::= : : :;::=A : : : :;::=@ : : : : :;::== : : :;::<A : :;:::> :;:::A : : &76-$% *-%$8("6 : : : :;::=A : : : : : : :;:::= :;:::E : : :;:::< :;:::? : :;:::E : : : : :;:::@ :;:::E :;:::= : : : : :;::=A : : :;:::= : : : : : :;:::@ : : : : : :;:::= :;:::E : : : : #'&3/ : : : :;:::= : : : :;:::< : : : :;:::C : : : : :;:::< : : :;:::E : :;:::= :;:::> : : FIGURE 3: Function-Failure Mode Matrix Snippet In the component-failure mode matrix there were 41 components which had both failure mode and failure rate information. There also exist function-flows in the repository that have no observed occurrences. This results in some function-flows not having data. This can be seen in Figure 3 for export translational to acoustic. FFRDM can not provide data for these function-flows during the design process. Since there are often many components that are a solution to a function-flow, there are often several failure modes fit to each function-flow. In some cases there an even distribution of failure modes for that particular function-flow. For example, in the function-failure mode matrix convert electromagnetic to mechanical energy has 11 failure mode occurrences. Galling & Seizure has the lowest failure rate with a value equal to 0.0001 failures per million hours while wear has the highest with a value equal to 0.0015 failures per million hours. In this case there is no particular failure mode that would stand out to the designer as needing to be mitigated. This case makes it hard to provide any useful recommendations because none of the failure modes stand out beyond any other. In other cases there is one or two distinct failure modes for 41 a specific function-flow which stand out significantly. The failure mode creep for regulate solid has a value equal to 0.0219 failures per million hours. The next closest value is 0.0037 failures per million hours. Here the designer can see that the failure mode creep is the most likely to occur and would provide recommendations to mitigate this failure mode. In most cases there is a distribution of failure mode data. In this situation a few failure modes have either high or low likelihood values and several have moderate likelihood values. Figure 4 shows data for secure solid where 19 failure modes have been observed. Failure rate values range from 0.001 to 0.5901 failure per million hours. For this function-flow there is a single failure mode that stands out, wear, and several with moderate and low values. Recommendations would be provided to mitigate wear, cracking, and creep. Secure(Solid( wear" voiding" unknown" spalling" rupture" overstress"of"incorrect"cur"mag" other" noise" latchBup" impact" galling"and"seizure" fre@ng" fa9gue" ar9fact"failure" direct"chemical"a?ack" creep" cracking" corrosion" control"issue" contamina9on" breakdown" bonding"defect" 0" 0.1" 0.2" 0.3" 0.4" Failure(Rate((failures(per(million(hours)( FIGURE 4: Failure Mode Data for Secure Solid 0.5" 0.6" 42 4.2. Functional Failure Rate Design Method This method is used during the conceptual stage of design when the functional model is complete. The process to accomplish this is done in four steps. To validate the steps to use the FFRDM knowledge base, a past FFDM example has been revisited. In this example, FFDM was used during the design of a portable air compressor to provide recommendation that would mitigate potential failures. In this section it is used to outline the use of the four steps and the FFRDM knowledge base. Step 1: Import function-flows from the functional model Figure 5 shows the functional model for the portable air compressor. Portable Air Compressor Import Solid Mat. Couple Solid Mat. Import Rot. E. Convert Rot. E. to Pn. E Import Human Mat. Distribute Th. E. Guide Pn. E. Export Pn. E. Export Th. E. Import Gas Mat. Separate Gas Mat. Guide Gas Mat. Import Solid Mat. Stabilize Solid Mat. Export Solid Mat. Export Gas Mat. FIGURE 5: Functional Model for Portable Air Compressor This information is formatted into a table format as shown in Figure 6. It is important to notice the import solid appears twice in the functional model and twice in Figure 6. This must be true in order for step 3 of the methodology to generate accurate results. 43 !"#$%&'#()*'+ &,-'.%/012 &,-'.%/.'%1%&'#1* &,-'.%/3",1#/,1%4.&1* &,-'.%/2'*&5 &,-'.%/2'*&5 $'"-*4/2'*&5 $'#64.%/.'%1%&'#1*/%'/-#4",1%&$ 47-'.%/-#4",1%&$ 0"&54/-#4",1%&$ 5&2%.&8"%4/%34.,1* 47-'.%/%34.,1* 24-1.1%4/012 0"&54/012 47-'.%/012 2%18&*&94/2'*&5 47-'.%/2'*&5 FIGURE 6: FFDM Step #1 Snippet Step 2: Look up function-flows in the FFRDM knowledge base There will be several failure modes for each functional input and all should be recorded for the most complete results. A snippet of the result of step #2 is shown in Figure 7. Function(flow/Failure0Mode contamination control0issue corrosion cracking creep artifact0failure fatigue fretting import0gas 0.0001 0.0055 0.006 0.0018 0.0011 0.0036 0 0.0001 import0rotational 0.0001 0 0.0106 0.0081 0.0217 0.0214 0.0006 0.0019 import0human0material 0 0.0006 0.0033 0.023 0.0301 0.0732 0.022 0.0002 import0solid 0.0104 0.0043 0.0331 0.0494 0.0946 0.0662 0.0034 0.0035 import0solid 0.0104 0.0043 0.0331 0.0494 0.0946 0.0662 0.0034 0.0035 couple0solid 0.0211 0.0943 0.5681 0.0652 4.2447 3.7973 0.0134 0.1068 convert0rotational0to0pneumatic 0 0.0101 0.008 0.0004 0 0.0004 0 0 export0pneumatic 0 0.0101 0.009 0.0012 0.0003 0.0018 0 0 guide0pneumatic 0 0.0006 0.0011 0.0014 0.0009 0.0005 0 0 distribute0thermal 0.0002 0.0005 0.0029 0.0035 0.0031 0.004 0 0.0002 export0thermal 0.0002 0.0065 0.0105 0.0047 0.005 0.0066 0 0.0003 separate0gas 0 0 0 0 0 0 0 0 guide0gas 0.0002 0.0258 0.0221 0.0028 0.0014 0.0042 0 0.0001 export0gas 0.0002 0.0106 0.0104 0.0027 0.0015 0.0038 0 0.0001 stabilize0solid 0 0 0.0004 0.0001 0.0001 0.001 0 0 export0solid 0.0066 0.0028 0.023 0.0315 0.0628 0.0464 0.0023 0.0023 FIGURE 7: FFDM Step #2 Snippet Step 3: Sum failure rate data for each failure mode The failure rates in each column should be summed to yield a total failure rate for each failure mode. This step sets the stage to determine which failure modes the 44 designer should spend time to determine recommendations for. A snippet of this result can be seen in Figure 8. Function(flow/Failure0Mode contamination control0issue corrosion cracking creep artifact0failure fatigue fretting import0gas 0.0001 0.0055 0.006 0.0018 0.0011 0.0036 0 0.0001 import0rotational 0.0001 0 0.0106 0.0081 0.0217 0.0214 0.0006 0.0019 import0human0material 0 0.0006 0.0033 0.023 0.0301 0.0732 0.022 0.0002 import0solid 0.0104 0.0043 0.0331 0.0494 0.0946 0.0662 0.0034 0.0035 import0solid 0.0104 0.0043 0.0331 0.0494 0.0946 0.0662 0.0034 0.0035 couple0solid 0.0211 0.0943 0.5681 0.0652 4.2447 3.7973 0.0134 0.1068 convert0rotational0to0pneumatic 0 0.0101 0.008 0.0004 0 0.0004 0 0 export0pneumatic 0 0.0101 0.009 0.0012 0.0003 0.0018 0 0 guide0pneumatic 0 0.0006 0.0011 0.0014 0.0009 0.0005 0 0 distribute0thermal 0.0002 0.0005 0.0029 0.0035 0.0031 0.004 0 0.0002 export0thermal 0.0002 0.0065 0.0105 0.0047 0.005 0.0066 0 0.0003 separate0gas 0 0 0 0 0 0 0 0 guide0gas 0.0002 0.0258 0.0221 0.0028 0.0014 0.0042 0 0.0001 export0gas 0.0002 0.0106 0.0104 0.0027 0.0015 0.0038 0 0.0001 stabilize0solid 0 0 0.0004 0.0001 0.0001 0.001 0 0 export0solid 0.0066 0.0028 0.023 0.0315 0.0628 0.0464 0.0023 0.0023 Sum 0.0495 0.176 0.7416 0.2452 4.5619 4.0966 0.0451 0.119 FIGURE 8: FFDM Step #3 Snippet Step 4: Provide designer with recommendations based on summed failure rates To provide useful recommendations from the failure modes with high likelihood, definitions provided in the failure mode taxonomy must be consulted and additional research should be performed. Definitions in the taxonomy offer details on the physical phenomena that occurs during failure. Additional research can help the designer to understand how the high likelihood failure modes occur in a general sense. These were used to determine the additional recommendations in Table 3. 4.3. Design Recommendations To validate the FFRDM knowledge base, a past FFDM example was used. It should be noted that this was the design of a new product and was chosen to be compatible with information in the original FFDM knowledge base. The FFRDM knowledge base is not limited to failures from a specific domain and will offer information not seen by the previous knowledge base. FMEA was also performed in this example and compared with FFDM. It was determined that FFDM provides similar recommendations as FMEA as well as others which were not predicted by 45 FMEA [3]. Here, the analysis has been done using the FFRDM knowledge base to show that, in general, the same recommendations can be made as well as additional recommendations. Also, in section 4.4 the likelihood of the failures is discussed as a way to offer the designer information on which recommendations require more attention than others. This analysis shows that improvements in FFDM have been accomplished. This is done first by verifying the same recommendations can be obtained that were proposed by the original FFDM knowledge base. Table 2 shows the function-flows along with the original recommendations for the portable air compressor. TABLE 2: FFDM Example for a Portable Air Compressor Function-flow Recommendation Import Gas Import Rot.E. Import Hand Import solid Couple solid Convert Rot.E. to Pn.E. Export Pn.E. Guide Pn.E. Distribute Th.E. Export Th.E. Separate Gas Guide Gas Export Gas Stabilize Solid Export Solid - Choose materials that can properly interact with air and water - Perform fatigue analysis on rotating components and housing - Include a filter screen on air inlet - Include bearings to support shaft - Choose a flexible material for the exhaust tube - Fin the endplate for better heat transfer - Choose a hardened material with clamping flats for input shaft - Perform extensive stress analysis on support feet The recommendations provided in Table 2 were derived directly from the failure modes returned by the function-flows. These same function-flows were queried for the FFRDM knowledge base and returned all but one of the failure modes. The missing failure mode was yielding which correlated to the perform extensive stress analysis on support feet recommendation. Along with these, other failure modes were discovered for which recommendation should be provided. These include artifact failure, creep, and unknown. Unknown is listed as a failure mode with a high likelihood but 46 recommendations will not be provided since none can be derived. Recommendations that summarize these added failure modes can be found in Table 3. TABLE 3: Additional Recommendations for the Portable Air Compressor Failure Mode Artifact Failure Creep Recommendation - Research air intake and shaft support selection to mitigate artifact failure - Simulate design/build prototype to verify design - Inspect and evaluate periodically during manufacturing to mitigate error - Perform Finite Element Analysis to locate stress concentrations Artifact Failure, as described previously, is caused by either an artifact failing, a poor design, or poor workmanship during the building process. This information about artifact failure was used to reason about what recommendations should be offered to the designer. The first three recommendations address this. Creep can be described as the tendency of a solid material to undergo plastic deformation over time due to high material stress. Finite Element Analysis (FEA) can be used to identify these stresses bases on force inputs. It is recommended that once the design has geometry, FEA be performed. This can be done for a rough sketch or the final design. A variety of software packages can be used in conjunction with a solid modeling program to reduce high user workload during this process. For example, Patran is capable of importing Solidworks drawings, but can also be used to reproduce physical geometries for FEA. Although this recommendation does not mitigate a failure during functional design, it offers information during functional design that will be used to mitigate failure. 4.4. Failure Mode Likelihood Recommendations have been provided based on the FFRDM knowledge base by using the four step process. In this knowledge base a likelihood in the form of a 47 failure rate is provided for each failure mode. This is used to determine which failure modes should receive the most attention during design based on the likelihood of failure. The additional failure modes presented in section 4.3 were those with a high likelihood. Wear is the only original failure mode that was considered to have a high failure rate. The failure rates associated with the additional three failure modes along with four of the five in the original example are summarized in Table 4. The top four failure modes are significant because their failure rates are noticeably higher than the others. TABLE 4: Failure Rates of Failure Modes for Portable Air Compressor Failure Mode Unknown Creep Artifact Failure Wear Corrosion Fretting Fatigue Failure Rate (Failure per Million Hours) 5.2435 4.5619 4.0966 3.3714 0.7416 0.1190 0.0451 The predominate failures associated with air compressors include not building a sufficient amount of discharge air at the specified pressure, not being able to achieve the specified pressure, and bearing failures [33]. The first two are a direct result of wear in the valves. The failure mode wear was initially given by FFDM and was also given by FFRDM as one with a high likelihood. Also, bearing failure corresponds directly to artifact failure. The first recommendation in Table 3 provides mitigation for this failure event. Of the original failure modes proposed by FFDM, corrosion, fretting, and fatigue had a low likelihood of occurring. There are not related to predominate failure which leads to the conclusion that the recommendations associated with these failure modes are not likely to occur and can be discarded. Implementing likelihood to the failure modes reduces unnecessary work during the design process and steers designers to critical failure modes. 48 5. CONCLUSION The Functional Failure Rate Design Method was generated and presented to provide critical failure information in the conceptual design stage to reduce the likelihood of failure. The data in this knowledge base shows the likelihood that a function-flow fails in a specific failure mode and motivates reliability analysis at the early stage of design. The FFRDM knowledge base is an extension of FFDM. Failure rates of components have been added to make decisions for which failure modes should be prioritized. A significant increase in data has also been used to expand the knowledge base to provide robust results. To validate this addition, the FFRDM knowledge base was used on a past FFDM example of a portable air compressor. This analysis shows that improvements in FFDM have been accomplished by determining additional failure modes which were originally overlooked. Recommendations were provided for these failure modes. 6. FUTURE WORK The data presented in FMD-97 lists failure mode occurrences for specific components. In this research this data was converted from the listed failure modes in FMD-97 to a failure mode taxonomy. These taxonomies, Collin’s on mechanical failures and Stone and Tumer’s on both mechanical and electrical, list failure modes in a single level. Formatting the taxonomy in this manner assumes that all failure modes can be described at a single level. Although, if there is a lack of information at the time the failure is observed, the definitions provided in the current taxonomy would likely be too descriptive to adequately fit the failure. The failure mode taxonomy should be restructured to assume a hierarchal format. This provided two distinct advantages. First, when the failure is being inspected and recorded in to data records for use later, it will not be necessary to fit a failure to a failure modes that is more detailed than the inspection can offer. If only general information can be gathered about the failure, it should only be recorded in such a manner. The Reliability Information Analysis Center has also recognized this issue. Data that is not acquired to their standards must be discarded. A hierarchal structure for failure modes will result in data being recorded 49 more accurately, providing more data useable during the design process. The second advantage for a new format is that the designer can perform reliability analyses at different levels of abstraction. Failure modes can be viewed at the highest level as a material, energy, or signal failure. This structure will follow the functional basis. This offers designers direction and information for later reliability analyses. In addition, the FFRDM knowledge base should be entered in the repository in the Design Lab at OSU. This would take the next step to automate this process, reducing user workload to mitigate failure. 7. ACKNOWLEDGMENTS This research was funded in part by DARPA (Subaward to FA8650-10-C-7079 with Palo Alto Research Center). The opinions, findings, conclusions, and recommendations expressed are those of the authors and do not necessarily reflect the views of the sponsors. 50 breakdown contamination control'issue corrosion cracking creep artifact'failure fatigue fretting actuate allow change channel collect condition connect contain convert decrease decrement detect display distribute export extract guide import increase increment indicate inhibit join link measure mix position prevent process provision regulate remove rotate secure sense separate shape signal stabilize stop store supply support transfer translate transmit transport bonding'defect APPENDIX A: Fails/Mhours 1.0E94 0 1.4E92 0 0 0 0 0 9.0E94 0 0 0 0 7.0E94 1.4E93 0 3.4E92 1.5E93 0 0 0 0 3.0E94 0 0 1.0E94 5.8E93 0 0 0 2.3E93 0 0 7.7E93 0 0 0 0 0 3.0E94 0 2.0E94 0 1.3E92 0 5.0E94 0 0 0 0 0 0 0 0 0 1.0E94 0 0 0 0 0 2.0E94 0 2.0E94 9.0E94 0 0 0 0 0 0 0 0 2.2E93 0 0 0 0 0 0 1.0E93 0 0 0 0 0 0 2.3E93 2.3E93 0 1.0E93 0 0 0 1.1E93 0 3.2E93 0 0 0 0 0 9.5E93 0 0 0 0 1.0E93 1.7E92 0 1.2E92 2.2E92 0 1.0E93 0 0 1.0E94 0 0 0 2.1E92 0 1.0E93 0 1.6E92 0 0 2.4E92 7.6E93 3.5E93 0 0 0 3.0E94 6.8E93 4.5E93 1.0E94 1.3E92 0 1.0E94 0 3.2E92 9.0E94 7.6E93 0 2.0E94 0 0 0 2.8E91 0 0 2.0E94 5.8E93 1.3E92 8.3E92 0 1.2E91 3.3E92 0 1.0E94 8.1E93 0 1.1E93 0 0 6.0E94 4.5E92 6.0E94 3.0E94 0 1.7E92 0 1.0E92 1.1E91 4.9E93 6.0E94 3.8E93 0 2.0E94 9.1E93 1.2E92 6.0E93 0 1.1E91 0 7.4E93 5.0E93 1.7E92 4.5E93 1.1E91 0 0 4.0E94 1.2E93 2.0E94 3.6E91 0 0 0 1.0E92 3.1E92 1.3E91 4.0E94 4.4E91 1.0E91 0 0 1.5E92 2.2E93 1.1E92 4.5E93 0 7.0E94 2.2E91 1.6E93 0 0 4.1E92 7.0E94 8.0E93 2.6E91 7.2E93 7.0E94 6.8E93 2.0E94 4.0E94 6.6E92 1.2E92 8.4E93 4.7E93 2.5E91 0 2.1E92 4.0E93 2.4E93 0 4.9E92 0 7.2E93 8.0E94 3.0E94 0 5.4E92 0 0 0 2.6E93 2.3E92 1.2E91 7.0E94 2.2E91 1.7E91 0 0 1.0E92 4.0E94 9.2E93 7.2E93 0 2.0E94 2.2E91 3.0E94 5.6E93 0 1.0E92 0 4.0E94 3.8E91 3.0E93 7.7E93 1.8E93 0 1.0E94 8.6E92 1.6E92 1.3E93 7.0E94 5.5E92 0 7.4E93 2.0E94 5.4E93 6.0E94 1.2E91 1.0E94 2.4E93 3.0E93 1.0E94 0 1.4E91 0 0 0 6.6E92 2.0E92 2.1E91 3.0E94 4.3E91 2.8E91 0 0 9.3E92 1.1E93 2.6E92 2.5E93 0 6.0E94 3.2E91 3.0E94 0 0 6.5E92 7.5E93 0 3.6E91 4.6E92 1.9E92 4.4E92 0 1.0E94 1.0E91 3.2E92 2.7E92 1.5E93 1.4E91 0 7.4E92 0 5.7E92 4.0E94 8.1E92 1.0E94 5.0E94 5.6E93 7.0E94 4.0E94 1.6E91 0 0 5.0E94 1.9E93 1.7E92 2.2E91 0 4.4E91 3.2E91 0 7.0E94 1.3E92 4.4E93 3.3E92 1.0E94 0 5.0E94 4.1E91 3.5E93 1.2E93 0 6.2E92 6.6E93 4.0E94 2.4E91 1.7E92 6.5E93 1.2E93 4.0E94 1.5E93 7.8E92 3.1E92 2.8E92 3.2E93 1.8E91 0 1.6E92 2.0E94 9.0E94 0 1.9E92 0 0 0 0 0 1.2E92 0 0 0 0 1.0E93 2.6E92 0 7.2E92 4.5E92 0 0 1.7E93 0 4.0E94 0 0 1.0E94 4.5E92 0 0 0 4.1E93 0 0 2.4E92 1.7E93 8.0E94 0 0 0 1.6E93 0 3.0E94 8.0E94 2.7E92 0 7.0E94 0 4.0E94 0 4.7E92 0 0 1.2E93 0 0 4.1E93 0 0 0 0 3.0E93 7.5E93 0 1.1E91 9.1E93 0 0 1.0E94 0 1.6E93 0 0 4.0E94 2.8E92 0 0 0 8.5E93 2.0E94 0 2.1E92 0 1.0E94 0 0 0 1.0E93 6.0E94 1.3E93 1.0E94 4.2E92 0 2.5E93 0 51 %04-*+ 1-+*5:34 #"%2( "+5(, HC(,2+,(22'")' %#*",,(*+'*3,,(#+' 0-&#%+3$( ,34+3,( 3#.#"/# C"%$%#& /(-, -*+3-+( -11"/ *5-#&( *5-##(1 *"11(*+ *"#$%+%"# *"##(*+ *"#+-%# *"#C(,+ $(*,(-2( $(*,(0(#+ $(+(*+ $%241-D $%2+,%!3+( (E4",+ (E+,-*+ &3%$( %04",+ %#*,(-2( %#*,(0(#+ %#$%*-+( %#5%!%+ F"%# 1%#. 0(-23,( 0%E 4"2%+%"# 4,(C(#+ 4,"*(22 4,"C%2%"# ,(&31-+( ,(0"C( ,"+-+( 2(*3,( 2(#2( 2(4-,-+( 25-4( 2%&#-1 2+-!%1%G( 2+"4 2+",( 23441D 2344",+ +,-#2)(, +,-#21-+( +,-#20%+ +,-#24",+ &-11%#&'-#$'2(%G3,( APPENDIX A (continued): Fails/Mhours >7>9:< B789:; 67;9:= 8 6789:; 8 8 8 @789:= 8 8 6789:; =789:; 67<9:= >789:= 8 @769:= >7@9:= 8 <789:; ;789:; 6769:< =7<9:= 8 8 ?789:; A7=9:= ;789:; ;789:; 8 <7<9:= 8 8 >7?9:= 6789:< ;789:; =789:; 8 6789:; =7@9:= 6789:= B7?9:< 6789:; ?7;9:= 8 67>9:= 8 8 8 8 8 8 8 8 8 ;789:; 8 8 8 8 <789:; 67>9:< 8 6769:< 67>9:< 8 8 8 8 ;789:; 8 8 8 67<9:< 8 8 8 8 6789:; 8 6769:< 8 8 8 8 8 ;789:; <789:; <789:; 8 ?789:; 8 =789:; 8 8 8 8 8 8 8 8 8 =789:= 8 8 8 8 67<9:< ?7>9:< 8 >789:< 67=9:< 8 8 8 8 8 8 8 8 67<9:< 8 8 8 8 8 67=9:< ;7?9:< 8 8 8 8 8 8 67=9:< A789:; 8 >7?9:< 8 8 A789:; ?789:; ;789:; B7A9:< 8 8 8 8 8 <769:= 8 8 8 8 6769:< <769:< 8 <769:= =7?9:< 8 8 8 8 =789:; 8 8 6789:; 67=9:= 8 8 8 67?9:< 8 8 =769:= 8 8 8 8 8 8 8 6789:; 8 =7=9:= 8 <789:; 8 =7<9:= >789:; 67?9:= 8 8 8 =789:; 8 6769:6 8 8 8 =789:< B7?9:< ?789:= ;789:; @769:= ;7=9:= 8 <789:; <789:< <789:; ;7>9:< 6789:; 8 <789:; A7?9:= =789:; <789:; 8 67@9:= A789:; 67=9:< >7A9:= 67>9:< ?789:; 67;9:< 8 8 67>9:= 67B9:= 67>9:= 6789:; ?7>9:= 8 >7<9:< A789:; 67=9:6 B789:; 67?9:= 8 67@9:< B789:; 8 8 67@9:6 8 8 67@9:< 6789:; 6769:= B789:= 8 67A9:6 67>9:6 8 67>9:< ?7?9:< <789:; A7A9:< 8 8 =789:; =7=9:6 67<9:< ;7;9:< 8 ?7?9:= =789:; 67A9:< =769:6 67>9:= @789:; 8 B789:; =789:< 67>9:= 67?9:6 67;9:6 <789:; 67>9:6 8 >7?9:< B789:; A789:; 6789:; 67>9:= 8 8 8 6789:; 8 >7B9:< 8 8 8 8 67=9:< ?7<9:< 8 <7@9:= A7=9:< 8 8 =789:; 6789:; 67<9:< 8 8 =789:; 67;9:= 8 8 8 ;789:< ;789:; 8 67=9:= 8 =789:; 8 8 8 <769:< B789:; 6789:< 8 67B9:= 8 A789:; 8 ;7?9:= 67@9:< 67<9:6 6789:; @789:; =7A9:< ;789:; 6789:< =7>9:6 8 8 @789:; A7>9:= <789:= =7<9:6 6769:< ?769:6 =7>9:6 8 6789:; @7B9:= A7;9:< <7>9:= ;789:; 8 =7=9:< ;789:6 6789:= 6789:< 8 @7;9:= B7?9:< 8 <7?9:6 ?769:= 67=9:= ;7;9:= 6789:< <789:< 67;9:6 <7?9:= <789:= 67A9:< =789:6 8 B7>9:= =769:< 8 8 6789:; 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 6789:; 8 8 8 8 8 8 8 8 8 6789:; 8 8 8 8 8 8 ?7B9:= B789:; <7<9:6 =789:; 8 67A9:< =7?9:< ?789:; ;7=9:6 8 8 8 >769:< @7@9:= >789:6 ;7@9:< 67?9I8 @7;9:6 8 ;789:; <769:= A7;9:< ?769:= ?789:; 8 ;769:< @789:6 A7;9:< A789:< 8 6769:6 <7A9:< B789:; A7A9:6 67@9:= =7@9:= ;7B9:< ?789:; 67=9:< 67A9:6 ?7?9:= <769:= >7B9:< A7>9:6 8 6789:6 =7B9:= 52 CONCLUSION The effort to move reliability engineering into the early stage of design represents an increasing area of activity in engineering design. This research aims to meet this need using two methodologies. The first methodology uses a RBD approach during the functional stage of design. The second is a competitive alternative to functional FMEA. Both move the risk analysis from its typical embodiment/redesign stage to the front end of the design process. Currently, failure rate data is available for components. Engineers typically use component failure rates to evaluate design reliability or the mean-time-before-failure. In this research a method is developed to calculate function-flow failure rates using component failure rates. Using the Design Repository, a relationship was established between the function-flows and components. Values in the matrix indicate the number of occurrences where a component has solved a function-flow. Noise in the data was eliminated using the Heaviside function. Two separate rules were implemented to make this step systematic and logical. Component failure rates were shared with function-flows based on a weighted average calculation, or a minimum and maximum logic statement. This process can be reproduced using different components, component failure rates, functional languages, occurrence data, or Heaviside rules. Regardless, the outcome is a set of function-flow failure rates which can be implemented using the methodology to calculate system reliability during function design. The methodology presented in the first manuscript provides useful information to the designer during the function stage of design. This information can be used to investigate different functions in the functional model, or to meet reliability design requirements. The process to use the method consists of five steps and is performed once the functional model is complete. Examples of the methodology were compared with traditional RBDs. These show that minimum and maximum system reliability, using the function-flow failure rates, are always less than or greater than that of the traditional RBD. Also, in all three examples the weighted average reliability given by the methodology showed similar results to those from the component failure rates. 53 Each was within 13% of the other. The goal of the weighted average reliability was to mimic the reliability provided by the component RBD. In the second manuscript, improvements were made to an existing process to determine a relationship between functions and failure modes. The Design repository was used to acquire the link between functions and components. A comprehensive manual from the RIAC was used to generate a matrix linking components to failure modes. Values in this matrix are the number of occurrences where a component has failed in a certain failure mode. These occurrences were converted to failure rates by multiplying through component failure rates. The final step is to multiply the two matrices together. This returns a function to failure mode matrix. Any cell in this matrix represents the failure rate of a failure mode for a specific function. This data was calculated to be used in FFRDM, however the process to calculate the data can be redone using different initial data. Also in the second manuscript, FFRDM was presented to provide critical failure information in the conceptual design stage to reduce the likelihood of failure. The data in this knowledge base shows the likelihood that a function-flow fails in a specific failure mode and motivates reliability analysis at the early stage of design. The FFRDM knowledge base is an extension of FFDM. Failure rates of components have been added to make decisions for which failure modes should be prioritized. A significant increase in data has also been used to expand the knowledge base to provide robust results. To validate this addition, the FFRDM knowledge base was used on a past FFDM example of a portable air compressor. This analysis shows that improvements in FFDM have been accomplished by determining additional failure modes which were originally overlooked. Recommendations were provided for these failure modes based on definition in the failure mode taxonomy and knowledge about the product being designed. Both methods presented in this thesis are used in the early stage of design. Each method has specific capabilities, but each have the goal to provide designers information earlier in the design process. This type of information helps the designer 54 become aware of potential failures and what parts of the design these failures result from. Becoming aware of the potential failures is the first step to mitigating them. 55 VITA Bryan O'Halloran is currently a Master's of Science student in Mechanical Engineering at Oregon State University and holds a Bachelor's of Science degree in Engineering Physics from the same school. His current research interests are reliability engineering and functional design. 56 REFERENCES [1] Blanchard, B. S., 1992, Logistics Engineering and Management, Prentice-Hall, Inc., Englewood Cliffs. [2] Pahl, G., and Beitz, W., 1984, Engineering Design: A Systematic Approach, Design Council, London. [3] Stone, Robert B., Tumer, Irem Y., and Van Wie, M., 2005, "The Function-Failure Design Method," Journal of Mechanical Design, 127(3), pp. 397-407. [4] Crowell, W., Denson, W., Jaworski, P., and Mahar, D., 1997, "Failure Mode/ Mechanism Distribution 1997," Rome. [5] Carmignani, G., 2009, "An Integrated Structural Framework to Cost-Based Fmeca: The Priority-Cost Fmeca," Reliability Engineering and System Safety, 94(4), pp. 861-871. [6] Montgomery, T. A., and Marko, K. A., 1997, "Quantitative Fmea," Proc. Reliability and Maintainability Symposium, pp. 226-228. [7] Wirth, R., Berthold, B., Kramer, A., and Peter, G., 1996, "Knowledge-Based Support Analysis for the Analysis of Failure Modes and Effects," Engineering Applications of Artificial Intelligence, 9(3), pp. 219-229. [8] Price, C. P., 1996, "Effortless Incremental Design Fmea," Proc. Annual Reliability and Maintainability Symposium, Las Vegas, NV U.S.A. [9] Hunt, J. E., Pugh, D. R., and Price, C. P., 1995, "Failure Mode Effects Analysis: A Practical Application of Functional Modeling," Applied Artificial Intelligence, 9(1), pp. 33-44. [10] Hari, A., and Weiss, M. P., 1999, "Cfma-an Effective Fmea Tool for Analysis and Selection of the Concept for a New Product," Proc. ASME Design Engineering Technical Conference, Design Theory and Methodology Conference, Las Vegas, NV, DETC99/DTM-8756. [11] Eubanks, C. F., Kmenta, S., and Ishii, K., 1997, "Advanced Failure Modes and Effects Analysis Using Behavior Modeling," Proc. ASME Design Engineering Technical Conferences, Sacramento, CA, DETC97/DTM-3872. 57 [12] Kmenta, S., Fitch, P., and Ishii, K., 1999, "Advanced Failure Modes and Effects Analysis of Complex Processes," Las Vegas, NV. [13] Refaul Ferdous, F. K., Rehan Sadiq, Paul Amyotto, Brian Veitch, 2009, "Handling Data Uncertainties in Event Tree Analysis," Process safety and environmental protection, 87(5), pp. 283-292. [14] Kenarangui, R., 1991, "Event-Tree Analysis by Fuzzy Probability," IEEE Transactions on Reliability, 40(1). [15] Ming-Hung Shu, C.-H. C., Jing-Rong Chang, 2006, "Using Intuitionistic Fuzzy Sets for Fait-Tree Analysis on Printed Circuit Board Assembly," Microelectronics Reliability, 46(12), pp. 2139-2148. [16] H. Xu, L. X., R, Robidoux, 2009, "Drbd Dynamic Reliability Block Diagrams for System Reliability Modelling," International Journal of Computers and Application, 31(2), pp. 132-141. [17] Brall, A., Hagen, W., and Tran, H., 2007, "Reliability Block Diagram Modeling Comparisons of Three Software Packages," Proc. Reliability and Maintainability Symposium, pp. 119-124. [18] Bazu, M., 1995, "A Combined Fuzzy-Logic & Physics-of-Failure Approach to Reliability Prediction," Transactions on Reliability, 44(2), pp. 237-242. [19] Pfefferman, J. D., and Cernuschi-Frías, B., 2002, "A Non-Parametric NonStationary Procedure for Failure Prediction," Transactions on Reliability, 51(4), pp. 434-442. [20] Robert B. Stone, Irem Y. Tumer, Michael E. Stock, 2005, "Linking Product Functionality to Historic Failures to Improve Failure Analysis in Design," Research in Engineering Design, 16(2), pp. 96-108. [21] Robert B. Stone, Irem Y. Tumer., Michael Van Wie, 2004, "The Function-Failure Design Method," Mechanical Design, 127(3), pp. 397-407. [22] Daniel A. Mcadams, K. L. W., 2002, "A Quantitative Similarity Metric for Design-by-Analogy," Mechanical Design, 124(pp. 173-182. [23] William Denson, G. C., William Crowell, Amy Clark, Paul Jaworski, 1994, "Nonelectric Parts Reliability Data 1995," Rome. 58 [24] Kurtoglu, T., Campbell, M., Bryant, C., Stone, R. And Mcadams, D, 2009, "A Component Taxonomy as a Framework for Computational Design Synthesis," Computers and Information Science in Engineering, 9(1). [25] Tolga Kurtoglu, M. I. C., 2009, "An Evaluation Scheme for Assessing the Worth of Automatically Generated Design Alternatives," Research Engineering Design. [26] Ullman, D. G., 2010, The Mechanical Design Process, McGraw-Hill, Boston. [27] Stone, R., and Wood, K., 2000, "Development of a Functional Basis for Design," Journal of Mechanical Design, 122(4), pp. 359-370. [28] "Failure Mode/Mechanism Distribution 1997," Rome. [29] Uder, S. J., Stone, Robert B., and Tumer, Irem Y., 2004, "Failure Analysis in Subsystem Design for Space Missions," Proc. ASME Design Engineering Technical Conferences, Design Theory and Methodology, Salt Lake City, Utah, DETC2004/DTM-57338. [30] Kurtoglu, T., Campbell, M., Bryant, C., Stone, R., and Mcadams, D., 2005, "Deriving a Component Basis for Computational Functional Synthesis," Melbourne, Australia. [31] Collins, J. A., 1993, Failure of Materials in Mechanical Design, John Wiley & Sons, New York, NY U.S.A. [32] William Denson, G. C., William Crowell, Amy Clark, Paul Jaworski, 1994, "Nonelectric Parts Reliability Data 1995," Rome. [33] Kim, T. W., Singh, B., Sung, T. Y., Park, J. H., and Lee, Y. H., 1996, "Failure Mode, Effect and Criticality Analysis (Fmeca) on Mechanical Subsystems of Diesel Generator at Npp," Taejon.