Measurement and Analysis Interaction (A1)


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Measurement and Analysis Interaction (A1)

  1. 1. Measurement and Analysis Interaction (A1) Measure Hypothesize stratification factors Compute baseline metrics Study process and plan for measurement of Y variables Data Exploration: Find patterns related to treatment differences (i.e. stratification) Hypothesis Generation for X (cause) variables with no stratification Measure Hypothesis Generation for X (cause) variables within stratification Is there a stratification pattern? Are there new stratification factors to consider? NO NO YES Any probable stratifications within the re-focused data set? Verify Causes NO YES YES More measurements required? Measure YES NO
  2. 2. Output of Measurement Selection (A1) <ul><li>Project Y variable(s) (CTQ) identified and linked to problem/goal </li></ul><ul><li>At least one X variable (predictor) to help find cause of Y variable </li></ul><ul><ul><li>Start with stratification factor as initial type of X variable </li></ul></ul><ul><li>Plan for making sure you know: </li></ul><ul><ul><li>Where to collect measurements </li></ul></ul><ul><ul><li>Data is available </li></ul></ul><ul><ul><li>It is feasible (time, money, personnel) to collect data </li></ul></ul><ul><li>Exercise: CTQ Tree </li></ul><ul><li>Exercise: Measurement Assessment Tree </li></ul>
  3. 3. Output of Operational Definition (A2) <ul><li>Clear, concise, detailed, unambiguous description of what is being measured </li></ul><ul><ul><li>Definitions of key terms like defect, product and service </li></ul></ul><ul><li>Guidelines on how to interpret the routine and the unusual </li></ul><ul><li>Initial data collection plan for what (sets up the when and how) </li></ul><ul><ul><li>Use Operational Definition Worksheet (pg. 169) </li></ul></ul>
  4. 4. Output of Identifying Data Sources (A3) <ul><li>Identification of existing data sources that will meet some (or all) measurement needs. Criteria for acceptable existing data include: </li></ul><ul><ul><li>Used the same operational definitions developed for the project collection efforts (especially in agreeing with customer definitions) </li></ul></ul><ul><ul><li>Structured to support analysis stage (i.e. has required stratification factors) </li></ul></ul><ul><li>Identification of new data sources to needed to meet requirements </li></ul><ul><li>Validating of ability to access and sort existing data </li></ul>
  5. 5. Prepare Data Collection and Sampling Plan (A4) <ul><li>Identify/confirm stratification factors </li></ul><ul><ul><li>Must begin with some idea of the “end game” </li></ul></ul><ul><ul><li>Data exploration (analysis stage) lives or dies on decisions made here </li></ul></ul><ul><li>Develop sampling scheme </li></ul><ul><li>Create data collection forms </li></ul>
  6. 6. Developing the Sampling Scheme (A4.2) <ul><li>Choice – Population or Process sampling? </li></ul><ul><ul><li>Population sampling: Large (essentially infinite), homogeneous pool of data </li></ul></ul><ul><ul><li>Process sampling: Sample taken from a “running process stream” </li></ul></ul><ul><ul><li>Ref: Tables 9-1 and 10-2 and Figures 10-6 to 10-10 </li></ul></ul><ul><li>Accounting for “sampling bias” </li></ul><ul><ul><li>Bad sampling processes: convenience sampling and judgment sampling </li></ul></ul><ul><ul><li>Good sampling processes: systematic sampling, random sampling, stratified sampling </li></ul></ul><ul><li>Setting the Confidence Interval (CI) (Detailed discussion at end of Measure Stage of DMAIC model) </li></ul><ul><ul><li>Typical interval is set at 95% (this is Minitab default) </li></ul></ul><ul><ul><li>Must know something about process to ballpark the sample size for a 95% CI </li></ul></ul><ul><li>Exercise: Manual Sample size calculation (pg. 171-172) </li></ul>
  7. 7. Creating Data Collection Forms (A4.3) <ul><li>Avoiding pitfalls: </li></ul><ul><ul><li>KISS </li></ul></ul><ul><ul><li>Good labeling </li></ul></ul><ul><ul><li>Space for identifying data: date, time, collector </li></ul></ul><ul><ul><li>Have consistent structure </li></ul></ul><ul><ul><li>Include key STRATIFICATION FACTORS </li></ul></ul><ul><li>Types of collection forms: </li></ul><ul><ul><li>Check sheets </li></ul></ul><ul><ul><li>Data sheets </li></ul></ul><ul><ul><li>Travelers: Excellent method to “ pair data ” when stratification factor and Y-variable measurement don’t occur at same place and/or time </li></ul></ul>
  8. 8. Output of Data Collection and Sampling Plan (A4) <ul><li>A list of stratification factors </li></ul><ul><li>Completed sampling plan </li></ul><ul><li>Data collection forms </li></ul>
  9. 9. Output of Implement/Refine Measurement Process (A5) <ul><li>Review/finalize collection plan </li></ul><ul><ul><li>Perform Measurement System Analysis including Gage R&R, bias assessment, stability and linearity testing, and calibration </li></ul></ul><ul><li>Prepare workplace: Let all know what’s going on </li></ul><ul><li>Tested collection procedures: </li></ul><ul><ul><li>KISS and trial run </li></ul></ul><ul><ul><li>Validate collector training </li></ul></ul><ul><li>Collect data </li></ul><ul><li>Monitor measurement accuracy and refine </li></ul><ul><li>Exercise: Gage R&R Assessment (continuous and discrete) </li></ul>
  10. 10. Minitab Gage R&R Example
  11. 11. Minitab Gage R&R Session Window Gage R&R %Contribution Source VarComp (of VarComp) Total Gage R&R 0.0011386 98.84 Repeatability 0.0004267 37.04 Reproducibility 0.0007119 61.80 Operator 0.0006148 53.37 Operator*Part 0.0000972 8.44 Part-To-Part 0.0000133 1.16 Total Variation 0.0011519 100.00 Study Var %Study Var Source StdDev (SD) (6 * SD) (%SV) Total Gage R&R 0.0337433 0.202460 99.42 Repeatability 0.0206559 0.123935 60.86 Reproducibility 0.0266823 0.160094 78.62 Operator 0.0247942 0.148765 73.05 Operator*Part 0.0098586 0.059151 29.05 Part-To-Part 0.0036515 0.021909 10.76 Total Variation 0.0339403 0.203642 100.00 Number of Distinct Categories = 1
  12. 12. Calculate Baseline Sigma Levels (B1) <ul><li>Key definitions </li></ul><ul><ul><li>Unit: Item being processed (focus of the project) </li></ul></ul><ul><ul><li>Defect: Failure to meet customer expectation </li></ul></ul><ul><ul><li>Defect Opportunity: Chance for product/service to be defective </li></ul></ul><ul><li>Guidelines for “defect opportunity” definition </li></ul><ul><ul><li>Focus on “defects that are important to the customer” </li></ul></ul><ul><ul><li>Should reflect “number of places in the process where it can go wrong, NOT all the ways it can go wrong” </li></ul></ul><ul><ul><li>Focus on routine defects – i.e. don’t count the “rare event” </li></ul></ul><ul><ul><li>Group similar defects in a single “defect category” </li></ul></ul><ul><ul><li>Be consistent (within defect and across company) </li></ul></ul><ul><ul><li>Don’t change operation definition without compelling reason </li></ul></ul><ul><li>Simple 4-step process </li></ul><ul><ul><li>Exercise: Sigma Calculation Worksheet (pg. 178-179) </li></ul></ul>
  13. 13. Calculate Final and First-Pass Yield (B2) <ul><li>Looks at the internal structure of the process </li></ul><ul><li>Two different ways of looking at yield and process sigma: final yield and first-pass yield </li></ul><ul><li>Final yield: </li></ul><ul><ul><li>How many defect-free items emerge at the end of the process including those that were successfully reworked </li></ul></ul><ul><ul><li>Internal defects and their costs are hidden </li></ul></ul><ul><li>First-pass yield: </li></ul><ul><ul><li>Number of items that make it through entire process without any rework included </li></ul></ul><ul><ul><li>Same as Rolled Throughput Yield (RTY) </li></ul></ul>
  14. 14. Measuring the Cost of Poor Quality (B3) <ul><li>Cost is connected to, but not the same as defect counts or sigma levels </li></ul><ul><li>Translate defect data into Cost of Poor Quality (COPQ) </li></ul>
  15. 15. Output of Calculating the Performance Baseline <ul><li>Well defined units, defects and defect opportunity </li></ul><ul><li>Calculated baseline sigma level </li></ul><ul><li>Calculated final and/or first-pass yield for Y variable </li></ul><ul><li>Identified labor and material rework costs </li></ul><ul><li>Translated defects into dollars </li></ul>
  16. 16. Long-Term vs. Short-Term Variation <ul><li>Short-term variation is less than long-term </li></ul><ul><li>Process shift adjustment of 1.5 sigma </li></ul><ul><li>Short-term capability: The best possible if process is centered </li></ul><ul><li>Long-term capability: Sustained reproducibility of the process </li></ul><ul><li>The Z calculation and the Z table </li></ul>
  17. 17. Histogram and the Normal Distribution X -S -1.96S -3S +S +1.96S +3S (+2S) (-2S) Measurement Value Frequency of a Measurement Value
  18. 18. The “Z” Table Mean X -S -3S +S +3S Question 1: How many standard deviations are there between the mean and the reference measurement? Distance from red dashed line to the mean One Standard Deviation Z = Z = 1 std dev Z +1.96S (+2S) -1.96S (-2S) Distance from yellow solid line to the mean One Standard Deviation Z = Z = about 1.5 Z From Z Table, a value of 1.5 = .0668 or 6.68 percent of the area under the curve is to the right of the solid yellow line.
  19. 19. “Z” Table Examples X -S -2S -3S +S +2S +3S .5200 .5190 .5180 .5170 .5210 .5220 .5230 .5195 Inches Distance from red dashed line to the mean One Standard Deviation Z = Z = .5212 - .5200 .0010 Z = Z = 1.2 .5212 What percentage of measurements are to the left of the red dashed line? .5200 - .5195 .0010 Z = .5 P = 30.85% P = 11.51% What percentage of measurements are to the right of the solid yellow line?
  20. 20. “Z” Table Exercise X -S -2S -3S +S +2S +3S .5200 .5190 .5180 .5170 .5210 .5220 .5230 .5192 Inches Z = Z = Z = .5208 What percentage of measurements are to the left of the red dashed line? Z = What percentage of measurements are between the dashed and solid lines?