Certified Reliability Engineer Exam Preparation Presented at: 8th Annual Reliability & Maintainability Training Summit 3-4 Nov 2015 Dr Bill Wessels PE CRE Introductions Dr Bill Wessels PE CRE, Consulting Reliability Engineer • Mechanical Engineer • 40-years experience (1975 – present) You • • • • Employer Current Field: Engineering Discipline Experience in Years Dr Bill Wessels PE CRE CRE Exam Prearation 2 Test Question A. I can vote for an answer B. Not an answer an sw er 0% Dr Bill Wessels PE CRE CRE Exam Prearation Ic an No ta n an s fo ra n Answer Now vo te Response Counter w er 0% 3 30 Employer A. Government B. Government Contractor C. Private Sector CRE Exam Prearation Se ct or 0% Pr iv at e nm en t nm en t Go ve r Dr Bill Wessels PE CRE Answer Now Go ve r 0 of 1 0% Co nt ra ct or 0% 4 Current Field A. Design/Prototype Test B. Systems Engineering & Integration/ Development-Operational Test C. Sustainability for Fielded Systems 0% Su st ai na bi li ty fo rF ie ld ed In te gr at ... Sy st em s 0% ne er in g& ig n/ Pr CRE Exam Prearation Sy st em sE ng i Dr Bill Wessels PE CRE Answer Now De s Response Counter ot ot yp e Te st 0% 5 30 Engineering Discipline (BS Degree) Dr Bill Wessels PE CRE Answer Now Response Counter CRE Exam Prearation 0% 0% 0% 0% 0% 0% 0% 0% 0% vil Ch em ic a l Sy st em s In du st r Co ial m pu te r So ftw ar e Ph ys ics Ch em ist ry 0% Ci Mechanical Electrical Civil Chemical Systems Industrial Computer Software Physics Chemistry M ec ha ni ca l El ec tri ca l A. B. C. D. E. F. G. H. I. J. 6 30 Experience (in years since BS) 0–4 4–8 8 – 12 Over 12 – 12 – 0% Ov er CRE Exam Prearation 4 – 0 Dr Bill Wessels PE CRE 0% 8 Answer Now 0% 12 0% 4 Response Counter 8 A. B. C. D. 7 30 Goal Pass the exam The Certified Reliability Engineer Exam Duration: 4-hrs Number of Questions: 150 {that is 96-sec / question Multiple choice with 4 alternatives Coverage: The body of knowledge as described in the Certified Reliability Engineer Primer Open Book/Open Notes – Includes the ‘Primer’ without the question sheets and these notes Bring pencils, scratch paper, calculator Dr Bill Wessels PE CRE CRE Exam Prearation 8 Reliability Engineering Body of Knowledge Reliability Management Probability and Statistics for Reliability Reliability in Design and Development Reliability Modeling and Predictions Reliability Testing Maintainability and Availability Data Collection and Use Sum ??? Dr Bill Wessels PE CRE CRE Exam Prearation {19 questions {25 questions {25 questions {25 questions {23 questions {17 questions {18 questions 172 questions 9 Reliability Management Strategic Management Dr Bill Wessels PE CRE CRE Exam Prearation 10 Strategic Management Demonstrate how reliability engineering improves programs, processes, products and services Define and describe quality and reliability and how they relate to each other Demonstrate how reliability engineers interact with marketing, safety, product liability, engineering, manufacturing and logistics (analysis methods) Explain how reliability integrates with other development activities (program interactions) Explain reliability engineering role in determination of failure consequences and liability management (warrantee) Determine impact of failures on service and cost throughout product’s life-cycle Describe how reliability engineering provides feedback to determine customer needs and specify product and service requirements Interpret basic project management tools and tools: Gannt, PERT, Critical Path, QFD Dr Bill Wessels PE CRE CRE Exam Prearation 11 Strategic Management Examples of reliability program benefits include: A. Matching product design with customer’s application B. Applying predictive and preventive maintenance C. Optimize burn-in time D. All of the above Dr Bill Wessels PE CRE CRE Exam Prearation 12 Examples of reliability program benefits include: Response Counter Dr Bill Wessels PE CRE Answer Now CRE Exam Prearation 0% 0% 0% 0% M at ch in gp ro du ct Ap de pl yi sig ng n pr w it h ed ict c.. iv . e an d pr ev en Op t.. tim . ize bu rn - in tim e Al lo ft he ab ov e A. Matching product design with customer’s application B. Applying predictive and preventive maintenance C. Optimize burn-in time D. All of the above 13 30 Examples of reliability program benefits include: A. B. C. D. Matching product design with customer’s application Applying predictive and preventive maintenance Optimize burn-in time All of the above Key word(s); reliability program benefits Index lists page II-3 Dr Bill Wessels PE CRE CRE Exam Prearation 14 Dr Bill Wessels PE CRE CRE Exam Prearation 15 Reliability Management Reliability Program Management Dr Bill Wessels PE CRE CRE Exam Prearation 16 Reliability Program Management Terminology – reliability definitions Element of a reliability program • Design-for-Reliability • FRACAS Product life-cycle costs • • • • Life-cycle stages with relationship to reliability Maintenance costs Life expectation Duty cycle Design evaluation Requirements management Reliability training programs Dr Bill Wessels PE CRE CRE Exam Prearation 17 Reliability Program Management The usefulness of FMEA as a design tool is largely dependent on the _______________ of the communication within the design process: A. Existence B. Quantity C. Effectiveness D. Frequency Dr Bill Wessels PE CRE CRE Exam Prearation 18 The usefulness of FMEA as a design tool is largely dependent on the _______________ of the communication within the design process: Existence Quantity Effectiveness Frequency 0% CRE Exam Prearation 0% Fr eq ue nc y s Qu an tit y Ef fe ct iv en es Dr Bill Wessels PE CRE 0% Answer Now Ex i Response Counter 0% st en ce A. B. C. D. 19 30 The usefulness of FMEA as a design tool is largely dependent on the _______________ of the communication within the design process: A. B. C. D. Existence Quantity Effectiveness Frequency Key word(s); FMEA, communication, design process Index lists page II-11 Dr Bill Wessels PE CRE CRE Exam Prearation 20 Dr Bill Wessels PE CRE CRE Exam Prearation 21 Reliability Management Product Safety and Liability Dr Bill Wessels PE CRE CRE Exam Prearation 22 Product Safety and Liability Role of reliability engineering Ethical issues System safety program • Risk assessment tools o FMECA o PRAT o FTA Dr Bill Wessels PE CRE CRE Exam Prearation 23 Product Safety and Liability Reliability engineering applied failure consequences analysis to address: A. Product failure expectation B. Personal injury concerns C. Training requirements D. Product testing requirements Dr Bill Wessels PE CRE CRE Exam Prearation 24 Reliability engineering applied failure consequences analysis to address: Product failure expectation Personal injury concerns Training requirements Product testing requirements Dr Bill Wessels PE CRE CRE Exam Prearation Pe 0% 0% 0% co nc er ns nj ur y rs on al i ex ai lu re Answer Now Pr od uc tf Response Counter pe ct at io n 0% Tr ai ni ng re qu Pr ire od uc m en tt ts es tin g re qu ir e m en ts A. B. C. D. 25 30 Product Safety and Liability Reliability engineering applied failure consequences analysis to address: A. Product failure expectation B. Personal injury concerns C. Training requirements D. Product testing requirements Key word(s); Product safety, consequences Index lists page II-17 Dr Bill Wessels PE CRE CRE Exam Prearation 26 Dr Bill Wessels PE CRE CRE Exam Prearation 27 Probability and Statistics for Reliability Basic Concepts Dr Bill Wessels PE CRE CRE Exam Prearation 28 Basic Concepts Terminology – statistical definitions Basic probability concepts • • • • • • Independence Mutually exclusive Complementary Conditional Joint occurrence Expected value Discrete and continuous distributions • Binomial • Poisson (homogeneous & nonhomogeneous) • Exponential • Lognormal • Weibull • Normal • Bathtub curve Statistical Process Control • Terminology – SPC definitions • Relationship to reliability Dr Bill Wessels PE CRE CRE Exam Prearation 29 Reliability Terminology Table of contents and index have entry for “Reliability Terminology” Primer provides a multi-page table that includes all of the terms and definitions Dr Bill Wessels PE CRE CRE Exam Prearation 30 Dr Bill Wessels PE CRE CRE Exam Prearation 31 Basic Concepts Distinction between: • Mean • Point estimate of the mean • Measure of central tendency Dr Bill Wessels PE CRE CRE Exam Prearation 32 The measure of central tendency is: Mean Mode Median All of the above CRE Exam Prearation 0% of th e ab ov e 0% Al l Dr Bill Wessels PE CRE Answer Now 0% M ed ia n Response Counter M ea n 0% M od e A. B. C. D. 33 30 The Central Limit Theory A. Treats all sample data as normally distributed B. Is applicable to only normally distributed data C. States that the means of the samples are normally distributed D. None of the above on St ly at no es rm th al at ly th di e ... m ea ns of th e s.. . No ne of th e ab ov e as no rm al .. to ab le ap pl ic ll s am pl e da ta CRE Exam Prearation Is Dr Bill Wessels PE CRE Answer Now Tr ea ts a Response Counter 0% 0% 0% 0% 34 30 Dr Bill Wessels PE CRE CRE Exam Prearation 35 The measure of central tendency is: The range The Variance The interquartile range All of the above Dr Bill Wessels PE CRE CRE Exam Prearation 0% Al l of th e ra ng e ab ov e 0% in te rq ua rti le ria nc e Va Th e Answer Now Th e Response Counter 0% ra ng e 0% Th e A. B. C. D. 36 30 The measure of central tendency is: A. B. C. D. The range The variance The interquartile range All of the above Primer only mentions range and variance by finding page in index for “measure of central tendency”. But right answer is either one of the first three or D, yet A and B are correct, therefore the answer must be D. Dr Bill Wessels PE CRE CRE Exam Prearation 37 Shortcut Formula for Standard Deviation Given: • SX • SX2 •N Then: • Var = [SX2 – (SX)2/n]/(n-1) • Std Dev = sqrt(VAR) Dr Bill Wessels PE CRE CRE Exam Prearation 38 Find Std Dev Given SX = 35.8, SX2 = 257.14, n = 5 0.40299 0.812 0.203 0.451 0% 0% 0% 45 1 0. 20 3 0. 81 2 40 2 CRE Exam Prearation 0. Dr Bill Wessels PE CRE 0% Answer Now 99 Response Counter 0. A. B. C. D. 39 30 Find Std Dev Given SX = 35.8, SX2 = 257.14, n = 5 VAR = [SX2 – (SX)2/n]/(n-1) VAR = [257.14 – (35.8)2/5]/(5-1) = 0.812/4 = 0.203 Std Dev = sqrt(0.203) = 0.45056 A. B. C. D. 0.40299 – divided VAR by n = 5, not n-1 = 4 0.812 – did not divide numerator by n-1 0.203 – did not take sqrt of VAR 0.451 Dr Bill Wessels PE CRE CRE Exam Prearation 40 Probability Concepts Union of events – – stated as events A or B occur - Addition Intersection of events – – stated as events A and B occur – Multiplication Additive Rule P(A B) = P(A and B) = P(A) + P(B) – P(A and B) Multiplication Rule P(A B) = P(A or B) = P(A)P(B) Dr Bill Wessels PE CRE CRE Exam Prearation 41 Counting Permutation – number of ways that n items can be arranged taking them r at time where order matters nPr = n!/(n-r)! – NOTE: 0! = 1 • A B C can be arrange as ABC, ACB, BAC, BCA, CAB, CBA, AB, BA, AC, CA, BC, CB, A, B, C • Permutation of n = 3 at r = 3: 3P3 = 3!/(3-3)! = (3)(2)(1)/1 = 6 • Permutation of n = 3 at r = 2: 3P2 = 3!/(3-2)! = (3)(2)(1)/1 = 6 • Permutation of n = 3 at r = 1: 3P1 = 3!/(3-1)! = (3)(2)(1)/(2)(1) = 3 Dr Bill Wessels PE CRE CRE Exam Prearation 42 Counting Combination– number of ways that n items can be arranged taking them r at time where order does not matter nCr = n!/r!(n-r)! – NOTE: 0! = 1 • • • • A B C can be arrange as ABC, AB, AC, BC, A, B, C Combination of n = 3 at r = 3: 3C3 = 3!/3!(3-3)! = (3)(2)(1)/(3)(2)(1) = 1 Combination of n = 3 at r = 2: 3C2 = 3!/2!(3-2)! = (3)(2)(1)/(2)(1) = 3 Combination of n = 3 at r = 1: 3C1 = 3!/1!(3-1)! = (3)(2)(1)/(2)(1) = 3 Dr Bill Wessels PE CRE CRE Exam Prearation 43 Advanced Concepts Statistical interval estimates • Confidence intervals • Tolerance intervals Hypothesis testing • • • • Means Variances Proportions Type I & II error Bayesian technique Dr Bill Wessels PE CRE CRE Exam Prearation 44 Dr Bill Wessels PE CRE CRE Exam Prearation 45 Dr Bill Wessels PE CRE CRE Exam Prearation 46 Dr Bill Wessels PE CRE CRE Exam Prearation 47 Dr Bill Wessels PE CRE CRE Exam Prearation 48 Dr Bill Wessels PE CRE CRE Exam Prearation 49 Given: Reliability of a part with an exponential reliability calculated to be 0.95 for a 10-hr mission duration. Find the reliability of the part for another mission given that the part has accumulated 100 hours (10 missions)? R(10|t = 100) R = 0.9510 R = 0.95 R > 0.95 Not enough Information Dr Bill Wessels PE CRE CRE Exam Prearation 0. 9 > R R = 0. 9 5 0% 0% In fo rm at io n R = 0. 9 51 0 Response Counter 0% 5 0% No te no ug h A. B. C. D. 50 30 Dr Bill Wessels PE CRE CRE Exam Prearation 51 Dr Bill Wessels PE CRE CRE Exam Prearation 52 Dr Bill Wessels PE CRE CRE Exam Prearation 53 Dr Bill Wessels PE CRE CRE Exam Prearation 54 Dr Bill Wessels PE CRE CRE Exam Prearation 55 Probability and Statistics for Reliability Statistical Inference Dr Bill Wessels PE CRE CRE Exam Prearation 56 Dr Bill Wessels PE CRE CRE Exam Prearation 57 Dr Bill Wessels PE CRE CRE Exam Prearation 58 Six test articles were put on test for 1000-hrs each with 2 failures with replacement. What is the point estimate of the MTBF. 500 1500 3000 6000 Dr Bill Wessels PE CRE CRE Exam Prearation 0% 0% 0% 60 00 0% 30 00 Answer Now 50 0 Response Counter 15 00 A. B. C. D. 59 30 Six test articles were put on test for 1000-hrs each with 2 failures with replacement. What is the point estimate of the MTBF. A. B. C. D. 500 1500 3000 6000 MTBF = nT/r = (6)(1000)/2 = 3000 Dr Bill Wessels PE CRE CRE Exam Prearation 60 Dr Bill Wessels PE CRE CRE Exam Prearation 61 Dr Bill Wessels PE CRE CRE Exam Prearation 62 The sample MTBF is 200 hrs with a standard deviation of 24 hrs. Sample size is 8 test articles. Find the 90% lower confidence limit for the MTBF given ta,n = 1.4 166.04 197.55 202.45 233.96 96 45 0% 23 3. CRE Exam Prearation 16 6. Dr Bill Wessels PE CRE 0% 20 2. Answer Now 0% 55 0% 04 Response Counter 19 7. A. B. C. D. 63 30 The sample MTBF is 200 hrs with a standard deviation of 24 hrs. Sample size is 8 test articles. Find the 90% lower confidence limit for the MTBF given ta,n = 1.4 A. B. C. D. 166.4 197.575 202.425 233.6 LCL = 200 – 1.4SQRT(24/8) = 197.575 Dr Bill Wessels PE CRE CRE Exam Prearation 64 Dr Bill Wessels PE CRE CRE Exam Prearation 65 Dr Bill Wessels PE CRE CRE Exam Prearation 66 Find the lower confidence limit for the MTBF for three test article failures for 1200 hours total test time. CRE Exam Prearation 0% 0% 0% 0% 12 00 Dr Bill Wessels PE CRE Answer Now 15 5 Response Counter 77 400 155 77 1200 40 0 A. B. C. D. 67 30 Find the 95% lower confidence limit for the MTBF for three test article failures for 1200 hours total test time. A. B. C. D. 400 155 77 1200 Chi-square from the table for a = 0.05 and 8 degrees of freedom (2r+2) is 15.5. MTBF = 2T/c2a,2r+2 = (2)(1200)/15.5 = 154.84 ~ 155. Dr Bill Wessels PE CRE CRE Exam Prearation 68 Dr Bill Wessels PE CRE CRE Exam Prearation 69 Dr Bill Wessels PE CRE CRE Exam Prearation 70 Dr Bill Wessels PE CRE CRE Exam Prearation 71 Dr Bill Wessels PE CRE CRE Exam Prearation 72 Reliability in Design and Development Reliability Design Techniques Dr Bill Wessels PE CRE CRE Exam Prearation 73 Reliability Design Techniques Use factors • Environmental o Temperature o Humidity o Vibration o Corrosive o Pollutants • Stresses o Static & dynamic loads o Severity of service o Electrostatic discharge o Radio frequency interference Stress-strength analysis FMEA in design Dr Bill Wessels PE CRE FTA in design Tolerance and worst-case analyses Robust design approaches (DOE) • Independent and dependent variable • Factors and levels • Error • Replication • Experimental design – full & fractional factorials Human factors reliability CRE Exam Prearation 74 Reliability in Design and Development Parts and Systems Management Dr Bill Wessels PE CRE CRE Exam Prearation 75 Parts and Systems Management Parts Selection Materials selection and control Derating methods and principles • S-N diagram • Stress-life relationship Establishing specifications Dr Bill Wessels PE CRE CRE Exam Prearation 76 Dr Bill Wessels PE CRE CRE Exam Prearation 77 Dr Bill Wessels PE CRE CRE Exam Prearation 78 Analysis finds part strength has a mean of 1200 with a std dev of 50. Mean stress is 900 with a std dev of 100. Find the reliability. 0% 0% 5 00 3 0. 99 6 CRE Exam Prearation 0. Answer Now 0. Dr Bill Wessels PE CRE 0% 0. 0% 3 Response Counter 75 0.9963 0.0037 0.75 0.5 7 A. B. C. D. 79 30 Analysis finds part strength has a mean of 1200 with a std dev of 50. Mean stress is 900 with a std dev of 100. Find the reliability. A. B. C. D. 0.9963 0.0037 - unreliability 0.75 =900/1200 0.5 =50/100 z = (1200 – 900)/sqrt(502 + 1002) = 2.68 U = 0.0037 from the standard normal table R = 1 – U = 0.9963 Dr Bill Wessels PE CRE CRE Exam Prearation 80 Reliability Modeling and Predictions Reliability Modeling Dr Bill Wessels PE CRE CRE Exam Prearation 81 Reliability Modeling Sources of reliability data Reliability block diagrams and models Simulation techniques Dr Bill Wessels PE CRE CRE Exam Prearation 82 Serial Assembly – Reliability Calculation Reliability Block Diagram Assembly LRU1 LRU2 LRUn n RASSY (t ) RLRUi t RLRU1 t RLRU 2 t i 1 Let: Then: R1(t) = 0.90 R2(t) = 0.95 R3(t) = 0.99 If: Then: RLRU n t R1(t) = R2(t) = R3(t) = R(t) = 0.95 RASSY(t) = (R(t))3 = (0.95)3 = 0.8574 RASSY(t) = (0.90)(0.95)(0.99) = R1(t)R2(t)R3(t) = 0.8465 Serial Design Configuration Reliability Rule-of-Thumb RASSY(t) ≤ MIN{Ri(t)} Dr Bill Wessels PE CRE CRE Exam Prearation 83 Given the following RBD, the assembly reliability is… 0.97 0.93 Greater than 0.97 Between 0.95 & 0.97 Between 0.93 & 0.95 Less than 0.93 CRE Exam Prearation 95 0. 93 0% Le s st ha n 0. & n 0. 93 & 95 0. n Be tw ee Dr Bill Wessels PE CRE 0% 0. 97 0. th an Answer Now Gr ea te r Response Counter 0% 97 0% Be tw ee A. B. C. D. 0.95 84 30 Given the following RBD, the assembly reliability is… 0.97 A. B. C. D. 0.95 0.93 Greater than 0.97 Between 0.95 & 0.97 Between 0.93 & 0.95 Less than 0.93 Dr Bill Wessels PE CRE CRE Exam Prearation 85 Given the following RBD, the assembly reliability is… 0.95 0.9999 0.857 0.925 CRE Exam Prearation 92 5 0% 0. 85 7 0% 0. 0. Dr Bill Wessels PE CRE 99 9 Answer Now 0% 9 0% 95 Response Counter 0. A. B. C. D. 86 30 Given the following RBD, the assembly reliability is… 0.97 A. B. C. D. 0.95 0.93 0.95 0.9999 0.857 0.925 R = (0.97)(0.95)(0.93) = 0.857 Dr Bill Wessels PE CRE CRE Exam Prearation 87 Serial Assembly – Equal Reliability Allocation Fault Tree Analysis Reliability Block Diagram Assembly in Down State Assembly OR LRU1 LRU1 Fails LRU2 Fails LRUn LRU3 Fails Given: n RASSY (t ) RLRU i (t ) i 1 RLRUi (t ) n RASSY (t ) Dr Bill Wessels PE CRE LRU2 RASSY(t) = 0.99884 nLRU = 3 Then: RLRU (t ) 3 0.99884 0.999628 CRE Exam Prearation 88 Find the reliability allocation for B, C & D in a serial design configuration given that the reliability requirement for A is 99% 0.97 0.996655 0.999999 0.785 99 6 99 9 0. CRE Exam Prearation 0. 0. Dr Bill Wessels PE CRE 0% 78 5 Answer Now 0% 0. 0% 99 9 0% 97 Response Counter 65 5 A. B. C. D. 89 30 Find the reliability allocation for B, C & D in a serial design configuration given that the reliability requirement for A is 99% A. B. C. D. 0.97 0.996655 0.999999 0.785 R Allocation = RA(1/n) = 0.99(1/3) = 0.996655 Note: RA = RBRCRD = R Allocation3 = 0.9966553 = 0.99 Dr Bill Wessels PE CRE CRE Exam Prearation 90 Serial System – Equal Reliability Allocation Rsys 0.99 n subsys 3 Rsubsys nsubsys Rsys 0.996655 n assy 3 Rassy nassy Rsubsys 0.998884 n LRU 3 RLRU Dr Bill Wessels PE CRE nLRU Rassy 0.999628 CRE Exam Prearation 91 Given the following RBD, the assembly reliability is… 0.97 0.95 0.93 st ha n 0. 93 & 0. 95 0. 93 0% Le s n 0. 95 & 0. th an 0% 0. 97 CRE Exam Prearation Be tw ee Dr Bill Wessels PE CRE Answer Now Gr ea te r Response Counter 0% 97 0% n Greater than 0.97 Between 0.95 & 0.97 Between 0.93 & 0.95 Less than 0.93 Be tw ee A. B. C. D. 92 30 Given the following RBD, the assembly reliability is… 0.97 0.95 A. B. C. D. Greater than 0.97 Between 0.95 & 0.97 Between 0.93 & 0.95 Less than 0.93 Dr Bill Wessels PE CRE 0.93 CRE Exam Prearation 93 Given the following RBD, the assembly reliability is… 0.97 0.95 0.93 st ha n 0. 93 & 0. 95 0. 93 0% Le s n 0. 95 & 0. th an 0% 0. 97 CRE Exam Prearation Be tw ee Dr Bill Wessels PE CRE Answer Now Gr ea te r Response Counter 0% 97 0% n Greater than 0.97 Between 0.95 & 0.97 Between 0.93 & 0.95 Less than 0.93 Be tw ee A. B. C. D. 94 30 Given the following RBD, the assembly reliability is… 0.97 0.95 A. B. C. D. 0.95 0.9999 0.857 0.925 0.93 R = 1 - (0.03)(0.05)(0.07) = 0.9999 Dr Bill Wessels PE CRE CRE Exam Prearation 95 Parallel Assembly Reliability Calculation Fault Tree Analysis Reliability Block Diagram Assembly in Down State Assembly AND LRU1 LRU1 Fails LRU2 Fails LRU2 LRU3 Fails 3 U ASSY (t ) U LRU i t U LRU1 t U LRU 2 t U LRU 3 (t ) LRU3 i 1 RASSY (t ) 1 U ASSY (t ) 1 U LRU1 t U LRU 2 t U LRU 3 (t ) U LRU (t ) 1 RLRU (t ) RASSY (t ) 1 1 RLRU1 (t ) 1 RLRU 2 (t ) 1 RLRU 3 (t ) Let: Then: R1(t) = 0.90 U1(t) = 0.10 R2(t) = 0.95 U2(t) = 0.05 R3(t) = 0.99 U3(t) = 0.01 UASSY(t) = (0.10)(0.05)(0.01) = 0.00005 RASSY(t) = 1 - UASSY(t) = 0.99995 If: Then: UASSY(t) = (U(t))3 = (0.05)3 = 0.000125 RASSY(t) = 1 - UASSY(t) = 0.999875 Parallel Design Configuration Reliability Rule-of-Thumb: Dr Bill Wessels PE CRE R1(t) = R2(t) = R(t) = 0.95 RASSY(t) ≥ MAX{Ri(t)} CRE Exam Prearation 96 Parallel Assembly Reliability Allocation Let: Rassy(t) = 0.99 Reliability Block Diagram Uassy(t) = 0.01 Then: Rassy 0.99 Assembly Uassy 1 Rassy 0.01 n LRU 3 LRU1 RLRU 1 LRU2 nLRU Uassy 0.785 OR LRU3 ULRU nLRU Uassy 0.215 RLRU 1 ULRU 0.785 Dr Bill Wessels PE CRE CRE Exam Prearation 97 Find the reliability allocation for B, C & D in a parallel design configuration given that the reliability requirement for A is 99% 0.97 0.996 0.999999 0.785 99 9 99 6 99 9 0. CRE Exam Prearation 0% 78 5 0% Answer Now 0. Dr Bill Wessels PE CRE 0% 0. 0% 97 Response Counter 0. A. B. C. D. 98 30 Find the reliability allocation for B, C & D in a parallel design configuration given that the reliability requirement for A is 99% A. B. C. D. 0.97 0.996 0.999999 0.785 R Allocation = 1-UA(1/n) = 1 – (1-0.99)(1/3) = 0.785 NOTE: RA = 1 – (1 – R Allocation)3 = 1 – (1 – 0.785)3 = 1 – (0.215)3 = 0.99 Dr Bill Wessels PE CRE CRE Exam Prearation 99 Parallel Design – Equal Reliability Allocation R (t ) 1 1 R t n ith Higher Level Design Configuration i j j Assume : R1 (t ) R2 (t ) jth Lower Level Design Configuration jth Lower Level Design Configuration jth Lower Level Design Configuration Rn (t ) Then : Ri (t ) 1 1 R j t n U j (t ) 1 R j t Ri (t ) 1 U j (t ) n U (t ) 1 R (t ) U (t ) 1 R (t ) n j i n n j n i n U i (t ) U j (t ) n 1 Ri (t ) n U i (t ) R j (t ) 1 U j (t ) Dr Bill Wessels PE CRE CRE Exam Prearation 100 Stand-by Design Logic Perfect Switch Imperfect Switch Primary Primary Stand-by Switch Normally Open Stand-by Primary Primary Stand-by Switch Normally Closed Stand-by Primary Primary Stand-by Switch Switch Engaged Dr Bill Wessels PE CRE Stand-by Fail Open Fail Closed Fail in Operation Mechanical – typically Weibull Digital – typically exponential Mechanical failure mode - evident to operator/maintainer Digital failure mode- hidden to operator/ maintainer Mechanical FD/FI - less potential for BIT/ BITE Digital FD/FI- high potential for BIT/ BITE Mechanical & digital subject to significant pre-Log downtime Mechanical subject to significant post-Log downtime CRE Exam Prearation 101 Equal Failure Rates – Perfect Switch Equal Failure Rates Perfect Switch Exponential Failure Model Primary Part Rassy ( ) R p ( ) 1 p SW Standby Part R p(|t) = 0.990050 p = 0.000125 p = 0.010000 = 80 1] Equal Failure Rate, Perfect Switch ( P = S) R(|t) = R p(|t)(1 + p) 0.999950 Dr Bill Wessels PE CRE CRE Exam Prearation 102 Unequal Failure Rates – Perfect Switch Unequal Failure Rates Exponential Failure Model Perfect Switch Primary Part p Rassy ( ) R p ( ) s p SW Standby Part R p(|t) = 0.990050 p = 0.000125 R s(|t) = 0.956571 s = 0.000555 R p ( ) Rs ( ) p/( s- p) = 0.290698 = 80 2] Unequal Failure Rate, Perfect Switch ( P < S) R(|t) = R p(|t) + [( p/( s - p)][R p(|t) - R s(|t)] 0.999782 Dr Bill Wessels PE CRE CRE Exam Prearation 103 Equal Failure Rates – Imperfect Switch Exponential Failure Model Primary Part Equal Failure Rates Imperfect Switch Rassy ( ) R p ( ) 1 Rsw ( ) p t SW Standby Part R p(|t) = 0.990050 p = 0.000125 p = 0.010000 = 80 R sw(|t) = 0.941765 3] Equal Failure Rate, Imperfect Switch ( P = S) R(|t) = R p(|t)[1 + R sw(|t) p] 0.999374 Dr Bill Wessels PE CRE CRE Exam Prearation 104 Unequal Failure Rates – Imperfect Switch Unequal Failure Rates Exponential Failure Model Imperfect Switch Primary Part p Rassy ( ) R p ( ) Rsw ( ) s p SW Standby Part R p(|t) = 0.990050 p = 0.000125 R s(|t) = 0.956571 s = 0.000555 R p ( ) Rs ( ) p/( s- p) = 0.290698 = 80 R sw(|t) = 0.941765 4] Unequal Failure Rate, Imperfect Switch ( P < S) R(|t) = R p(|t) + R sw(|t)[ p/( s - p)][R p(|t) - R s(|t)] 0.999215 Dr Bill Wessels PE CRE CRE Exam Prearation 105 Complex RBD – Cut Set Method A B E C Dr Bill Wessels PE CRE D Cut Set Terms AB CD AED CEB -ABCD -ABDE -ABCE -ACDE -BCDE -(2)ABCDE +(4)ABCDE A B C 0.96 0.95 0.94 0.96 0.95 0.94 0.96 0.95 0.94 0.96 0.95 0.94 0.96 0.95 0.96 0.95 0.94 0.96 0.94 0.95 0.94 0.96 0.95 0.94 0.96 0.95 0.94 CRE Exam Prearation D E Path 0.93 0.97 R/U 0.91 0.93 0.87 0.93 0.97 0.87 0.97 0.87 0.93 -0.80 0.93 0.97 -0.82 0.97 -0.83 0.93 0.97 -0.81 0.93 0.97 -0.81 0.93 0.97 -1.55 0.93 0.97 3.09 Reliability = 0.994 106 Reliability Modeling and Predictions Reliability Predictions Dr Bill Wessels PE CRE CRE Exam Prearation 107 Reliability Predictions Part count and part stress analysis Advantages and limitations Reliability prediction methods Reliability apportionment and allocation Dr Bill Wessels PE CRE CRE Exam Prearation 108 Parts Count Method for MTBF & MTTR A B C D Assembly MTBF by Parts Count Method Part MTBF FR n nFR A 1000 0.0010 1 0.0010 B 300 0.0033 2 0.0067 C 500 0.0020 4 0.0080 D 200 0.0050 3 0.0150 SFR = 0.0113 SnFR = 0.0307 MTBF = 32.61 Dr Bill Wessels PE CRE CRE Exam Prearation MTTR MTTR FR*MTTR 2.5 0.0025 3 0.0100 5 0.0100 1 0.0050 SFR*MTTR = 0.0275 MTTR = 2.4265 109 Reliability Testing Reliability Test Planning Dr Bill Wessels PE CRE CRE Exam Prearation 110 Reliability Test Planning Elements of a reliability test plan Types and applications of reliability testing Test environment considerations Dr Bill Wessels PE CRE CRE Exam Prearation 111 Dr Bill Wessels PE CRE CRE Exam Prearation 112 Dr Bill Wessels PE CRE CRE Exam Prearation 113 Reliability Testing Developmental Testing Dr Bill Wessels PE CRE CRE Exam Prearation 114 Development Testing Accelerated life test – ALT • Single stress • Multiple stress • Sequential stress Step stress testing – HALT Reliability growth testing • AMSAA • Duane • TAAF Software testing • White box • Fault injection Dr Bill Wessels PE CRE CRE Exam Prearation 115 Reliability Testing Product Testing Dr Bill Wessels PE CRE CRE Exam Prearation 116 Product Testing Assess purpose, advantage and limitations • Qualification/demonstration testing o Sequential o Fixed length • Product reliability acceptance test – PRAT • Stress screening o ESS o HASS o Burn-in • Attribute testing o Binomial o Hypergeometric • Degradation testing • Software testing Dr Bill Wessels PE CRE CRE Exam Prearation 117 Dr Bill Wessels PE CRE CRE Exam Prearation 118 Maintainability and Availability Management Strategies Dr Bill Wessels PE CRE CRE Exam Prearation 119 Management Strategies Maintainability and availability planning Maintenance strategies • Corrective maintenance – reactive • Preventive maintenance – proactive o RCM Maintainability apportionment/allocation Availability tradeoffs Dr Bill Wessels PE CRE CRE Exam Prearation 120 Availability A = Uptime/(Uptime + Downtime) Dr Bill Wessels PE CRE CRE Exam Prearation 121 Maintainability and Availability Analyses Dr Bill Wessels PE CRE CRE Exam Prearation 122 Analyses Maintenance time distributions • Lognormal • Weibull Preventive maintenance (PM) analysis • Tasks • Intervals • Non-applicability Corrective maintenance (CM) analysis • Fault isolation time – AKA FD/FI • Repair/replace time • Skill level Testability Spare parts strategy Dr Bill Wessels PE CRE CRE Exam Prearation 123 Data Collection and Use Data Collection Dr Bill Wessels PE CRE CRE Exam Prearation 124 Data Collection Types of data • Attribute (discrete) v continuous • Compete v censored Data sources Collection methods Data management • Acquisition • Media • Database Dr Bill Wessels PE CRE CRE Exam Prearation 125 Data Collection and Use Data Use Dr Bill Wessels PE CRE CRE Exam Prearation 126 Data Use Analysis • Algorithmic • Graphic FOR • Math Modeling • Trend Analysis • ANOVA Measures of effectiveness Dr Bill Wessels PE CRE CRE Exam Prearation 127 Data Collection and Use Data and Failure Analysis Tools Dr Bill Wessels PE CRE CRE Exam Prearation 128 Data and Failure Analysis Tools FMEA Criticality analysis • Hazards analysis • Severity analysis • Consequences analysis FTA FRACAS Dr Bill Wessels PE CRE CRE Exam Prearation 129