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Converting Measurement Systems From Attribute
- 1. The Statistical Engineering Process Simple Understanding Listen to the customer Observe the failure Measure the contrast Converge to the major influence Confirm the major influence Implement control 165 Complex Problems Statistical Engineering
- 2. Measure the Relationship How can we measure the contrast between a desirable Y-response ¡. And an undesirable Y-response¡¡¡ ¡° An attribute Measurement can be used to describe a problem. A variable Measurement is usually required to solve it. How else can you tell if you are headed in the right direction?¡± jdg 168
- 3. Relationship of Responses Linear Sensory Scoring 166 This is done¡ After the ¡°Y-Response¡± has been identified After a 30 piece initial contrasting samples have been identified with a customer ¡°Threshold¡± sample for ¡°Y-Response¡± To transform an Attribute Measurement into An Integer Range For Initial measurement of contrast to get problem started How ¡ Remember the Attribute Methodology Decide if any sample is Better or Worse than a standard Create a Linear scale with 6 increments of Resolution Relationship of Linear Sensory Methodology for Transformation: Collect 30 samples of Y-Response including Best sample of the Day Worst sample of the Day Customer Threshold sample Place Best, Threshold and Worst samples in Line Identify Y-Response lower mid point sample between Best and Threshold Identify Y-Response upper mid point sample between Threshold and Worst Place all reference samples in a line form Best to Worst and assign values 0.5, 1.5, 2.5, 3.5, 4.5 from Best to Worst Collect 30 samples with a full range of one day¡¯s variability Select a sample and compare it to the Threshold 2.5 If Better, compare it to the 1.5. If Worse compare it to the 3.5. Continue comparison until comparison reverses result. Scoring for sample will be 0, 1, 2, 3, 4, 5 based on last comparison made before result reversed (see illustration). 9) Repeat steps 7) and 8) for all remaining 29 samples.
- 4. Linear Sensor Scoring System 176 Linear Transformation values 0, 1, 2, 3, 4, 5 (6 distinct increments of resolution) 0 1 2 3 4 5 Linear Sensor Scoring Step 2 Step 1 Step 2 Step 3 Step 4 Step 7 Step 8 2.5 3.5 4.5 1.5 0.5 Threshold Lower Mid Upper Mid Best Worst 1 st Decision 2 nd Decision 2 nd Decision 3 rd Decision 3 rd Decision Better Worse Decision Time Sample
- 5. ? R Linear Sensory Measurement System (Verification of Discrimination Ratio) 176 Verify Measurement System: ( ? M / ? R = Repeatability Ratio ¨C Same Operator) ?? M / ? R = Reproducibility Ratio ¨C 2x Operators) If 1 st Measurement vs 2 nd Measurement: Do not Differ by more than 1 point Accept Repeatability 1/6 = 17% Error max. Differ by more than 1 point Reject Measurement System 2/6 = 34% Error min. Plot 1 st vs 2 nd Measurement (30 samples) Calculate ? M/ ? R . 1 st Linear Score 2 nd Linear Score Step 1 Plot 1 st Linear Score vs 2 nd Linear score
- 6. Using a Linear Scoring Options: Limited discrete variable data analyses (only good for initial contrast comparison with low resolutions) Capability Study (see below illustration) 2 sample t-tests ( difference in averages and/or variation) Distribution analyses (normal vs bi-modal vs others) Linear Sensor Scoring System Analyses
- 7. Take 2 contrasting Y-Respone samples and perform a preliminary stress vs strain analyses to understand the appropriate transformation type with good resolution potential. Decide on Transformation Method Stress Constant ¨C Measure Strain Strain Constant ¨C Measure Force Breaking strength If you use force that exceeds the Elastic Limit (distortion of original past the yield strength),you will need to measure the same event with 2 different measuring systems to perform a measuring system analyses. Examples: Cracked housings, UTS of materials, fatigue strength, etc. Forming Operations, joining operations, destructive testing, etc. Timed events, such as machine cycle, operator cycle, etc. Test protocol needs to be defined, to reduce unnecessary variation. Write out a procedure that can be forllowed by anyone gathering data. Measurement system validation using a scatter plot can be performed for the event (using 2 measurements of each event ¨C repeatability) or to validate the test protocol (using 2 operator independent of each other ¨C reproducibility) Rules - Use of ¡°Energy Aggravation¡± ( for Measurement System Transformation) 177
- 8. 3 Energy Transformations #1 1) Elastic Limit 1 2 UTS 3) Failure Strength 3 3 Transformation Applications #2 Pull to Constant Stress Measure Force Pull with Constant Force Measure Strain 3) Failure Strength = Breaking Strength
- 9. Examples: Gap between Material and surround: Constant Stress Identified as Best Tool Develop Test Protocol for non destructive pull test using constant force within Elastic limit of system Using a wedge gage, repeat test protocol for 2 nd measurement of each sample set up for ? M analyses Create representative sampling plan Run 30 piece Capability Study Identify contrast for analyses phase Use Multi-vari to separate w/pc, pc/pc, t/t groups How to apply the logic: 3 Transformation Applications Plastic Limit 1 lb. Wedge Gage Gap Within Elastic Limit ?
- 10. Examples: Accumulation of Dirt over Time (e.g for Paint Line Contamination): Constant Strain (Exposure over a constant Time) Identified as Best Tool Develop Test Protocol for using constant force such as exposure (or Time) to measure displacement (or accumulation of dirt) Using a piece of paper, repeat test protocol for 2 nd measurement of each location for ? M analyses Create representative sampling plan Run 30 piece Capability Study Identify contrast for analyses phase Use Multi-vari to separate w/pc, pc/pc, t/t groups How to apply the logic: 3 Transformation Applications Location #1 Location #3 Location #4 Location #2
- 11. Examples: Egg Shell robustness issue: Failure Strength Identified as Best Tool Develop Test Protocol for destructive method Place egg on scale and add Point source load onto egg measure force 2x for each destruction event (E.g. Known weight vs Scale) for ? M analyses Create representative sampling plan Run 30 piece Capability Study Identify contrast for analyses phase Use Multi-vari to separate w/pc, pc/pc, t/t groups How to apply the logic: 3 Transformation Applications
- 12. Energy Transformation Measurement System Scatter Plot ? R ? M ? R ? M X 100% = % Repeatability Pass : if = / or Less Than 17% Improve Measurement System : if Over 17%