Chapter 5 Basic Tools Introduction • Chapters 2 and 3 discussed histograms, sample mean, sample standard deviation, attribute/continuous data, and special/common cause. • This chapter continues the discussion of basic techniques and offers a collection of data analysis, data presentation, and improvement alternatives. • A wide variety of tools are briefly described for the purpose of aiding with the efficient building of strategies for collecting and compiling information that leads to knowledge. With this knowledge we can make better decisions. • Problem identification, defining, and solving. Introduction • Descriptive statistics help pull useful information from data; • Probability provides, a basis for inferential statistics and sampling plans. Introduction 7 management tools (7M tools) or 7 management and planning tools (7 MP tools). • affinity diagrams • interrelationship digraphs • tree diagrams • prioritization matrices • matrix diagrams • process decision program charts (PDPC) • activity network diagrams Introduction 7 quality control tools: • cause-and-effect diagram • check sheet • scatter diagram • flowchart • Pareto chart • histogram • control chart Introduction Tools working with ideas: • Activity network diagram • Affinity diagram • Benchmarking • Brainstorming • Cause-and-effect diagram • Flowchart • Force field • Interrelationship digraph (ID) • Matrix diagram nominal group technique (NGT) • Prioritization matrices • Process decision program chart (PDPC) • Tree diagram • Why-why diagram Introduction Tools working with numbers: • Check sheets • Control chart • Histogram • Pareto chart • Probability plot • Run chart • Scatter diagram 5.1 Descriptive Statistics S4/IEEE Application Examples • Random sample of last year’s invoices where the number of days beyond the due date was measured and reported (i.e., days sales outstanding [DSO]) • Random sample of parts manufactured over the last year, where the diameters of the parts were measured and reported 5.1 Descriptive Statistics • Sample Mean: Arithmetic average of the data values (x1, x2, x3 ,..., xi), which is mathematically expressed đ đ=1 đĨđ đĨ= đ • Sample Median (đĨ_50): the number at (n+1)/2 rank • TrMean (trimmed mean): Average of the values remaining after both 5% of the largest and smallest values, rounded to the nearest integer, are removed. • Sample standard deviation (SD) 1 đ−1 đ ( đđ đ=1 − đ )2 = 1 ( đ−1 đ đđ 2 −đđ 2 ) đ=1 5.1 Descriptive Statistics • SE mean (standard error of mean): • • • • đđˇ đ Minimum: lowest number in data set Maximum: largest number in data set Q1: first quartile Q3: third quartile 5.2 Run Chart (Time Series Plot) S4/IEE Application Examples • One random paid invoice was selected each day from last year’s invoices where the number of days beyond the due date was measured and reported (i.e., days sales outstanding [DSO]). The DSO for each sample was plotted in sequence of occurrence on a run chart. • One random sample of a manufactured part was selected each day over the last yean where the diameters of the parts were measured and reported. The diameter for each sample was plotted in sequence of occurrence on a run chart. 5.2 Run Chart (Time Series Plot) • A run chart permits the study of observed data for trends or patterns over time. • Can be used to compare a performance measurement before and after a solution implementation to measure its impact. • 20~25 points are needed to establish pattern and baselines. • Problem exists with the interpretation of run chart: all variation as important (over-reacting) ī control charts 5.2 Run Chart (Time Series Plot) www.pqsystems.com/.../chart_BasicRunChart.png 5.3 Control Chart S4/IEE Application Examples • One paid invoice was randomly selected each day from last year’s invoices where the number of days beyond the due date was measured and reported (i.e., days sales outstanding [DSO]). The DSO for each sample was plotted in sequence of occurrence on a control chart. • One random sample of a manufactured part was selected each day over the last year, where the diameters of the parts were measured and reported. The diameter for each sample was plotted in sequence of occurrence on a control chart. 5.3 Control Chart • Control limits are a function of data variability, not specification limits. • It gives not only process monitoring and control, but also direction for improvements. • It can separate special cause from common causes • Early identification of special causes • 94% of the troubles belong to system (common cause); only 6% are special cause (Deming 1986) • Monitoring should be of KPIVs (not only on KPOVs) • If process is shown to be in-control, issues should be looked collectively over some period of time ī Process Improvement techniques 5.3 Control Chart http://support.sas.com/rnd/app/qc/qc/shwclms.gif 5.4 Probability Plot • Probability plots are most often associated with tests to assess the validity of normality assumptions. • When data are a straight line on a normal probability plot, the data are presumed to be from a normal distribution. • Probability plots also apply to other distributions, such as the Weibull distribution. • Probability plots can also be used to make percentage of population statements (very useful in describing the performance of business and other processes) 5.4 Probability Plot Minitab: Graph Probability Plot • Single 5.5 Check Sheets • Check sheets contain the systematic recording and compiling of data from historical or current observations. • The information can indicate patterns and trends. • After agreement is reached on the definition of events or conditions, data are collected over a period of time and presented in tabular form. Problem Week Total 1 2 3 A /// //// // 10 B / // // 5 C //// / / 6 5.5 Check Sheets http://www.asq.org/learn-about-quality/datacollection-analysis-tools/overview/check-sheet.html 5.6 Pareto Chart S4/IEE Application Examples • Transactional workflow metric (could similarly apply to manufacturing; e.g., inventory or time to complete a manufacturing process): Random sample of last year’s invoices where the number of days beyond the due date was measured and reported (i.e., days sales outstanding [DSO] ). If an invoice was beyond 30 days late, it was considered a failure or defective transaction. A Pareto chart showed the frequencies of delinquencies by company invoiced. 5.6 Pareto Chart S4/IEE Application Examples • Transactional quality metric: Random sample of last year’s invoice, where the invoices were examined to determine if there were any errors when filling out the invoice or within any other step of the process. Multiple errors or defects could occur when executing an invoice. The total number of defects when the invoice was executed was divided by the total number of opportunities for failure to estimate the defect per million opportunity (DPMO) rate of the process. A Pareto chart showed the frequencies of delinquencies by type of failure. 5.6 Pareto Chart S4/IEE Application Examples • Manufacturing quality metric: Random sample of printed circuit boards over the last year, where the boards were tested for failure. The number of defective boards was divided by the sample size to estimate the defective rate of the process. A Pareto chart showed the frequencies of defective units by printed circuit board type. • Manufacturing quality metric: Random sample of printed circuit boards over the last year, where the boards were tested for failure. Multiple failures could occur on one board. The total number of defects on the boards was divided by the total number of opportunities for failure (sum of the number of components and solder joints from the samples) to estimate the defect per million opportunity (DPMO) rate of the process. A Pareto chart showed the frequencies of defects by failure type. 5.6 Pareto Chart • The Pareto principle basically states that a vital few of the manufacturing process characteristics cause most of the quality problems on the line, while a trivial many of the manufacturing process characteristics cause only a small portion of the quality problems. • Pareto chart may need to consider data from different perspectives. [by machine, or by shift] 5.6 Pareto Chart Coffee Pareto Chart 1400 100.0% 90.0% RANK 1200 80.0% 1000 70.0% 800 60.0% 50.0% 600 40.0% 400 30.0% 20.0% 200 0 10.0% Coffee Type Coffee Amount Grind Time Brew Time Water Temp Cup Size Cup Type 320 280 176 174 144 112 104 Percentage 24.4% 21.4% 13.4% 13.3% 11.0% 8.5% 7.9% Cumulative % 24.4% 45.8% 59.2% 72.5% 83.5% 92.1% 100.0% Count 0.0% 5.6 Pareto Chart: Procedure 1. Define the problem and process characteristics to use in the diagram. 2. Define the period of time for the diagram—for example, weekly, daily, or shift. 3. Total the number of times each characteristic occurred. 4. Rank the characteristics according to the totals from step 3. 5. Plot the number of occurrences of each characteristic in descending order in a bar graph form along with a cumulative plot of the magnitudes from the bars. 6. Trivial columns can be lumped under one column designation; however, care must be exercised not to forget a small but important item. 5.7 Benchmarking • • • Benchmarking involves the search of an organization for the best practices, adaptation of the practices to its processes, and improving with the focus of becoming the best in class. Benchmarking can involve comparisons of products, processes, methods, and strategies. Sources of information for benchmarking include the Internet, in-house published material, professional associations, universities, advertising, and customer feedback. http://totalqualitymanagement.files.wordpress.com /2008/11/picture24.png 5.7 Types of Benchmarking • • • • Internal benchmarking makes comparisons between similar operations within an organization. Competitive benchmarking makes comparisons with the best direct competitor. Functional benchmarking makes comparisons of similar process methodologies. Generic benchmarking makes comparisons of processes with exemplary and innovative processes of other companies. 5.8 Brainstorming • • Very valuable means of generating new ideas and involving a group. Many ways • to conduct a brainstorming session • to compile the information from the session http://www.howtoplaza.com/wpcontent/uploads/2010/05/productive-brainstorming-session.png 5.8 Brainstorming Formal process of brainstorming • Setup: • Table arranged in a manner to encourage discussion • Problem or question is written down for everyone to see • Basic rules: 1. Ask each member in rotation for one idea 2. Rule out all evaluations or critical judgments 3. Encourage wild ideas 4. Encourage good-natured laughter and informality 5. Target for quantity, not quality 6. Look for improvements and combinations of ideas 5.8 Brainstorming Guideline for the leader: 1. The problem needs to be simply stated. 2. Two or more people should document the ideas in plain sight so that the participants can see the proposed ideas and build on the concepts. 3. The name of the participant who suggested the idea should be placed next to it. 4. Ideas typically start slowly and build speed. Change in speed often occurs after someone proposes an offbeat idea. This change typically encourages others to try to surpass it. 5. A single session can produce over 100 ideas, but many will not be practical. 6. Many innovative ideas can occur after a day or two has passed. 5.8 Brainstorming • A follow-up session can be used to sort the ideas into categories and rank them. • When ranking ideas, members vote on each idea that they think has value. • For some idea considerations it is beneficial to have a discussion of the pros and cons before the vote • A circle is drawn around the ideas receive the most votes • Through sorting and ranking, many ideas can be combined while others are eliminated 5.8 Brainstorming Applications • • • • Problem definition Factors within a DOE Test strategy Inputs to the cause-and-effect diagram 5.9 Nominal Group Technique (NGT) Nominal group technique expedites team consensus on relative importance of problems, issues, or solutions. • An NGT is conducted by displaying a generated list of items, perhaps from a brainstorming session, on a flipchart or board. • Eliminating duplications and making clarifications, then creates a final list. • The new final list of statements is then prominently displayed, each item is assigned a letter, A, B ,... • On a sheet of paper, each person ranks the statements, assigning the most important a number equal to the number of statements and the least important the value of one. • Results from the individual sheets are combined to create a total overall prioritization number for each statement. 5.9 Nominal Group Technique (NGT) http://www.wsa-intl.com/Portals/70018/images/202.jpg 5.10 Force Field Analysis Force field analysis can be used to analyze what forces in an organization are supporting and which are restraining progress. • After an issue or problem is identified, a brainstorming session is conducted to create a list of driving forces and then a list of restraining force. • A prioritization is then conducted of the driving forces that could be strengthened. • There is then a prioritization of the restraining forces that could be reduced to better achieve the desired result. 5.10 Force Field Analysis Restraining Forces Action Items Create reward and recognition programs that reinforce Programs reinforce the old the new People do not have skills sets needed Create training programs so that people have the to succeed opportunity to learn new Introduce new vocabulary so people know you are Phrases still refer to the old speaking of the new Current cultural supports staying the Change culture so that it supports the new same People concerned about making Reassure them that mistakes are learning mistakes opportunities and failure will not be punished People concerned how changes Provide information that clarifies how performance will affect their job be evaluated People isolated in the ways they are Celebrate successes going about the new People wonder how serious the Provide consistent communications that clarify how company is about this change serious the company is about completing this change 5.11 Cause-and-Effect Diagram S4/IEE Application Examples • An S4/IEE project was created to improve the 30,000 footlevel metric days sales outstanding (DSO). A process flowchart was created to describe the existing process. A team created a cause-and-effect diagram in a brainstorming session to trigger a list of potential causal inputs and improvement ideas. • An S4/IEE project was created to improve the 30,000 footlevel metric, the diameter of a manufactured part. A process flow chart was created to describe the existing process. A team created a cause-and-effect diagram in a brainstorming session to trigger a list of potential causal inputs and improvement ideas. 5.11 Cause-and-Effect Diagram • also known as an Ishikawa diagram (after its originator Karoru Ishikawa) or fishbone diagram. • This technique is useful to trigger ideas and promote a balanced approach in group brainstorming sessions in which individuals list the perceived sources (causes) of a problem (effect). • A cause-and-effect diagram provides a means for teams to focus on the creation of a list of process input variables that could affect key process output variables. • Addresses strata issues based on key characteristics (e.g., who, what, where, and when). 5.11 Cause-and-Effect Diagram • When constructing a cause-and-effect diagram, it is often appropriate to consider six areas of causes that can contribute to an effect: materials, machine, method, personnel, measurement, and environment. • Each one of these characteristics is then investigated for sub-causes. Sub-causes are specific items or difficulties that are identified as a factual or potential cause to the problem (effect). 5.11 Cause-and-Effect Diagram Variations in creating a cause-and-effect diagram: • A team may choose to emphasize the most likely causes by circling them. • it can also be beneficial to identify noise factors (n) (e.g., ambient room temperature and a raw material characteristic that cannot be controlled), and factors that can be controlled (c) (e.g., process temperature or speed) by placing the letter n or c next to the named effect. • Include score with an importance and ease-of-resolution matrix. Cause-Effect (CE) Analysis www.syncfusion.com/.../img/Fishbone_larger.png 5.11 Cause-and-Effect Diagram Impact Impl High Low Easy 1 2 Hard 3 4 5.12 Affinity Diagram Affinity diagram can organize and summarize the natural grouping from a large number of ideas and issues. • Boldly record each brainstorming idea individually on a post note, using at a minimum a noun and verb. • Next, place the post note on a wall and ask everyone, without talking, to move the notes to the place where they think the issue best fits. • Upon completion of this sorting, create a summary or header sentence for each grouping. (Create subgroups for large groupings as needed with a subhead description.) • Connect all finalized headers with their groupings by drawing lines around the groupings. Affinity Diagram http://www.asq.org/learnabout-quality/ideacreationtools/overview/affinity.html 5.12 Affinity Diagram • • • • • • • • • • • Infrastructure Align projects with business needs Create system to pull projects from business metrics needs Establish project accountability Plan steering committee meetings Select champions, sponsors, and team leaders Determine strategic projects and metrics Communication plans Incentive plans Schedule project report outs Champion/sponsor training Compile lessons learned from past projects Project Execution • Project scoping • Project approval • Phase report outs • Project closure • Project leveraging • • • • Training Champion training Black belt training Green belt training Use training material w/roadmap • • • • Culture Create buy-in Evaluate obstacles and facilitate change Integrate 6σ into daily activities Communication plan 5.13 Interrelationship Digraph (ID) Interrelationship digraph permits systematic identification, analysis, and classification of cause-and-effect relationships, enabling teams to focus on key drivers or outcomes to determine effective solutions. • Assemble a team of 4 to 6 members • Arrange the 5-25 items from another tool (e.g., an affinity diagram) in a circular pattern on a flipchart. • Draw relationship between the items by choosing any one of the items as a starting point, with a stronger cause or influence indicated by the origination of an arrow. 5.13 Interrelationship Digraph (ID) • Upon the completion of a chart, get additional input from others and then tally the number of outgoing and input arrows for each item. • A high number of outgoing arrows indicates that the item is a root cause or driver that should be addressed initially. • A high number of incoming arrows indicates a key outcome item. • A summary ID shows the total number of incoming and outgoing arrows next to each item. • Driver and outcome items can be highlighted using a double box or bold box. 5.13 Interrelationship Digraph (ID) http://www4.asq.org/blogs/statistics/Images/Interrelationship.jpg 5.14 Tree Diagram • Tree diagrams can help people uncover, describe, and communicate a logical relationship that is hierarchical between important events or goals. • Similarly, a tree can describe the hierarchy that leads to a desirable or undesirable event. (fault tree or FT). • With this approach a big idea or problem is partitioned into smaller components. • Logical operators such as AND or OR gates can connect lower elements to higher elements in the hierarchy. 5.14 Tree Diagram 5.14 Tree Diagram http://www.conceptdraw.com/resources/images/solutionsscreens/business/Root_Cause_Tree_Diagram.png 5.15 Why-Why Diagram • A variation of the cause-and-effect diagram and tree diagram (Higgins 1994; Majaro 1988). • These final responses can be used as wisdom of the organization inputs for further investigation. WhyWhy Diagram http://www.syque.com/improvement/images/image343.gif 5.16 Matrix Diagram and Prioritization Matrices • A matrix diagram is useful to discover relationships between two groups of ideas. • A prioritization matrix quantifies and prioritizes items within a matrix diagram: activities, goals, or characteristics • Applications: cause-and-effect matrix and quality function deployment (QFD) 5.16 Matrix Diagram and Prioritization Matrices • Within a prioritization matrix, one can assign relative importance weights. • Simply assigned by the organization or team. • Other techniques: The analytical hierarchy process (AHP) • Within the AHP approach, a number of decisionmakers can integrate their priorities into a single priority matrix using a pairwise fashion. • This result of this matrix is a prioritization of the factors. 5.16 Analytical Hierarchy Process (AHP) A A. Fire in the belly B C D E B2 A2 A2 A3 B1 B2 B3 C1 C3 B. Soft skill C. Project management D. Analytical skill D2 E. Statistical knowledge A. Fire in the belly B. Soft skill C. Project management D. Analytical skill E. Statistical knowledge A B C D E 1 1/2 2/1 2/1 3/1 1 1/1 2/1 3/1 1 1/1 3/1 1 2/1 1 5.16 Analytical Hierarchy Process (AHP) A B C D E 1 1/2 2/1 2/1 3/1 B. Soft skill 2/1 1 1/1 2/1 3/1 C. Project management 1/2 1/1 1 1/1 3/1 D. Analytical skill 1/2 1/2 1/1 1 2/1 E. Statistical knowledge 1/3 1/3 1/3 1/2 1 A B C D E A. Fire in the belly A. Fire in the belly 1.0000 0.5000 2.0000 2.0000 3.0000 B. Soft skill 2.0000 1.0000 1.0000 2.0000 3.0000 C. Project management 0.5000 1.0000 1.0000 1.0000 3.0000 D. Analytical skill 0.5000 0.5000 1.0000 1.0000 2.0000 E. Statistical knowledge 0.3333 0.3333 0.3333 0.5000 1.0000 5.16 Analytical Hierarchy Process (AHP) A B C D E Sum Weights A. Fire 5.0000 5.0000 7.5000 8.5000 17.5000 43.5000 0.2652 B. Soft 6.5000 5.0000 9.0000 10.5000 19.0000 50.0000 0.3049 C. Project 4.5000 3.7500 5.0000 6.5000 12.5000 32.2500 0.1966 D. Ana skill 3.1667 2.9167 4.1667 5.0000 10.0000 25.2500 0.1540 E. Stat 1.7500 1.4167 2.1667 2.6667 13.0000 0.0793 5.0000 164.0000 5.17 Process Decision Program Chart (PDPC) • A process decision program chart (PDPC) helps with the organization and evaluation of processes and the creation of contingency plans. • PDPC can help anticipate deviations from expected events and provide insight to the creation of effective contingency plans. • PDPC can help determine the impact of problems or failures on project schedules. Specific actions can be undertaken for problem prevention or mitigation of impact when they do occur. • Subjective probabilities of occurrence can be assigned and then used for the assignment of priorities. 5.17 Process Decision Program Chart (PDPC) Berger et al. (2002) highlight the following steps, which are common to all PDPC formats: • Identify the process purpose. • Identify the basic activities and related events associated with the process. • Annotate the basic activities and related events. • Superimpose the possible (conceivable) deviations. • Annotate the possible deviations. • Identify and annotate contingency activities. • Weight the possible contingencies. 5.17 Process Decision Program Chart (PDPC) 5.17 Process Decision Program Chart (PDPC) http://www.syque.com/quality_tools/tools/TOOL S12_files/image002.gif 5.18 Activity Network Diagram or Arrow Diagram • Activity network diagrams (arrow diagrams) help with the definition, organization, and management of activities with respect to time. • The arrow diagram is used in program evaluation and review technique (PERT) and critical path method (CPM) methodologies. 5.18 Activity Network Diagram or Arrow Diagram Equipment testing and modification 2 Final debugging Dummy Equipment installation 1 6 System development 3 Manual Testing 5 System Training 7 System changeover System Testing Job training Position recruiting 4 Orientation Dummy 8 9 5.19 Scatter Diagram (Plot of Two Variables) S4/IEE Application Examples • An S4/IEE project was created to improve the 30,000-footlevel metric, days sales outstanding (DSO). A process flowchart was created to describe the existing process. A team created a cause-and-effect diagram in a brainstorming session to trigger a list of potential causal inputs and improvement ideas. One input that the team thought could be an important cause was the size of the invoice. A scatter diagram of DSO versus size of invoice was created. 5.19 Scatter Diagram (Plot of Two Variables) S4/IEE Application Examples • An S4/IEE project was created to improve the 30,000-footlevel metric, the diameter of a manufactured part. A process flowchart was created to describe the existing process. A team created a cause-and-effect diagram in a brainstorming session to trigger a list of potential causal inputs and improvement ideas. One input that the team thought could be an important cause was the temperature of the manufacturing process. A scatter diagram of part diameter versus process temperature was created. 5.19 Scatter Diagram (Plot of Two Variables) • A scatter diagram (plot) assesses the relationship between two variables (follow-up procedure to validate the consensus relationship from a cause-and-effect diagram) • 50 to 100 pairs of samples should be plotted • the independent variable is on the x-axis while the dependent variable is on the y-axis. • A scatter diagram relationship does not predict a true cause-and-effect relationship. • The plot only shows the strength of the relationship between two variables • The correlation and regression techniques can be used to test the statistical significance of relationships. 5.19 Scatter Diagram (Plot of Two Variables) 5.20 Example 5.1: Improving a Process that has Defects 5.20 Example 5.1: Improving a Process that has Defects • From p-chart, the process is in control; no special causes are noted. • Defect rate is too high 5.20 Example 5.1: Improving a Process that has Defects From 3200 manufactured PCBs 5.20 Example 5.1: Improving a Process that has Defects • A brainstorming session with experts in the field could then be conducted to create a cause-and-effect diagram for the purpose of identifying the most likely sources of the defects. • Regression analysis followed by a DOE might then be most appropriate to determine which of the factors has the most impact on the defect rate. • After Changes are made to the process • New Pareto chart to identify the next major cause • Control charts to monitor the “insufficient solder” problem 5.21 Example 5.2: Reducing Total Cycle Time of A Process • Development cycle time: 2~3 years • Survey indicates the biggest deterrent is “procurement of standard equipment and components”. • Loss time and revenue due to delay is 22 times higher than the equipment itself. 5.22 Example 5.3: Improving A Service Process • cycle time in a claim processing center, accounts payable organization, or typing center. • Current process flow • Cause-and-effect diagram for improvement opportunities • Pareto chart: simple solution • Benefit/Cost analysis (B/Cīģ96)