IENG 486 - Lecture 15

1. IENG 486 - Lecture 15 Gage Capability Studies IENG 486 Statistical Quality & Process Control

2. Bonus Points # 3 • In teams of 4 people, go to the Project Office and perform a gage R & R study on the 7 parts. • Half of the teams measured with the micrometer • Half of the teams measured with the dial calipers • Entire team works together to analyze the data – for the 4 Operators, estimate: • σ2 total • σ2 repeatability • σ2 reproducability • σ2 product • P/T for gage, assuming USL – LSL = 0.005” IENG 486 Statistical Quality & Process Control

3. Bonus Points # 4 • In teams of 4 people, go to the CIM Lab (CM 203) and set up a control chart strategy for the “pipe-bomb” machine. • Dr. Jensen will demonstrate the system, each team operates afterward. • The team will collect data using the scale, and track the data using the spreadsheet template, each control chart should have 30 samples. • Entire team works together to collect and analyze the data for the system, and to create and interpret x – and R – charts. • For the lab exercise, briefly report: • What your control chart strategy is (what did you measure and why) • Turn in print out of your trial control charts, and describe how the limits were developed • For each control chart, use your Trial Control Limits* on all 30 sample points, and interpret each chart for control using the 4 Western Electric Rules: • Convert your Trial Control Limit data to Standards • Circle Western Electric Rule violations, and describe what they show IENG 486 Statistical Quality & Process Control

4. Gage Capability Studies • Ensuring adequate gage and inspection system capability • In any problem involving measurement the observed variability in product is due to two sources: • Product variability - σ2product • Gage variability - σ2gagei.e., measurement error • Total observed variance in product: σ2total = σ2product + σ2gage (system) IENG 486 Statistical Quality & Process Control

5. e.g. Assessing Gage Capability • Following data were taken by one operator during gage capability study. IENG 486 Statistical Quality & Process Control

6. e.g. Assessing Gage Capability Cont'd • Estimate standard deviation of measurement error: • Dist. of measurement error is usually well approximated by the Normal, therefore • Estimate gage capability: • That is, individual measurements expected to vary as much as owing to gage error. IENG 486 Statistical Quality & Process Control

7. Precision-to-Tolerance (P/T) Ratio • Common practice to compare gage capability with the width of the specifications • In gage capability, the spec width is called the tolerance band • (not to be confused with natural tolerance limits, NTLs) • Specs for above example: 32.5 ± 27.5 • Rule of Thumb: • P/T  0.1 Adequate gage capability IENG 486 Statistical Quality & Process Control

8. Estimating Variance Components of Total Observed Variability • Estimate total variance: • Compute an estimate of product variance • Since : IENG 486 Statistical Quality & Process Control

9. Gage Std Dev Can Be Expressed as % of Product Std Dev • Gage standard deviation as percentage of product standard deviation : • This is often a more meaningful expression, because it does not depend on the width of the specification limits IENG 486 Statistical Quality & Process Control

10. Using x and R-Charts for a Gage Capability Study • On x chart for measurements: • Expect to see many out-of-control points • x chart has different meaning than for process control • shows the ability of the gage to discriminate between units (discriminating power of instrument) • Why? Because estimate of σx used for control limits based only on measurement error, i.e.: IENG 486 Statistical Quality & Process Control

11. Using x and R-Charts for a Gage Capability Study • On R-chart for measurements: • R-chart directly shows magnitude of measurement error • Values represent differences between measurements made by same operator on same unit using same instrument • Interpretation of chart: • In-control: operator has no difficulty making consistent measurements • Out-of-control: operator has difficulty making consistent measurements IENG 486 Statistical Quality & Process Control

12. Repeatability & Reproducibility:Gage R & R Study • If more than one operator used in study then measurement (gage) error has two components of variance: σ2total = σ2product + σ2gage σ2reproducibility + σ2repeatability • Repeatability: • σ2repeatability - Variance due to measuring instrument • Reproducibility: • σ2reproducibility - Variance due to different operators IENG 486 Statistical Quality & Process Control

13. Ex. Gage R & R Study • 20 parts, 3 operators, each operator measures each part twice • Estimate repeatability (measurement error): • Use d2 for n = 2 since each range uses 2 repeat measures IENG 486 Statistical Quality & Process Control

14. Ex. Gage R & R Study Cont'd • Estimate reproducibility: • Differences in xi operator bias since all three operators measured the same parts • Use d2 for n = 3 since Rx is from sample of size 3 IENG 486 Statistical Quality & Process Control

15. Ex. Gage R & R Study Cont'd • Total Gage variability: • Gage standard deviation (measurement error): • P/T Ratio: • Specs: USL = 60, LSL = 5 • Note: • Would like P/T < 0.1 IENG 486 Statistical Quality & Process Control

16. Comparison of Gage Capability Examples • Gage capability is not as good when we account for both reproducibility and repeatability • Train operators to reduce σ2reproducability = 0.1181 • Since σ2repeatability = 1.0195 (largest component), direct effort toward finding another inspection device. IENG 486 Statistical Quality & Process Control