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TN7: Basic Forms of Statistical Sampling for Quality Control

TN7: Basic Forms of Statistical Sampling for Quality Control. Acceptance Sampling: Sampling to accept or reject the immediate lot of product at hand. Statistical Process Control (SPC): Sampling to determine if the process is within acceptable limits. Acceptance Sampling. Purposes

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TN7: Basic Forms of Statistical Sampling for Quality Control

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  1. TN7: Basic Forms of Statistical Sampling for Quality Control • Acceptance Sampling: Sampling to accept or reject the immediate lot of product at hand.Statistical Process Control (SPC): Sampling to determine if the process is within acceptable limits.

  2. Acceptance Sampling • Purposes • Determine quality level • Ensure quality is within predetermined level Lot received for inspection Sample selected and analyzed Results compared with acceptance criteria Accept the lot Reject the lot Send to production or to customer Decide on disposition

  3. Basic Forms of Variation - SPC • Assignable variation is caused by factors that can be clearly identified and possibly managed. • Common variation is inherent in the production process.

  4. Control Limits are based on the Normal Curve x m z -3 -2 -1 0 1 2 3 Standard deviation units or “z” units.

  5. x LCL UCL Control Limits If we establish control limits at +/- 3 standard deviations, then we would expect 99.7% of our observations to fall within these limits

  6. StatisticalProcessControl See Exhibit S6.3 for other evidence prompting investigation

  7. Statistical Process Control (SPC) Charts UCL Normal Behavior LCL 1 2 3 4 5 6 Samples over time UCL Possible problem, investigate LCL 1 2 3 4 5 6 Samples over time UCL Possible problem, investigate LCL 1 2 3 4 5 6 Samples over time

  8. Statistical Sampling--Data Attribute (Go no-go information) • Defectives • Defects • Typically use sample size of 50-100 Variable (Continuous) • Usually measured by the mean and the standard deviation • Typically use sample size of 2 to 10

  9. Statistical Process Control:Attribute Measurements (P-Charts) Where Z is equal to the number of Standard Deviations

  10. 1. Calculate the sample proportion, p, for each sample.

  11. 2. Calculate the average of the sample proportions. 3. Calculate the sample standard deviation. 4. Calculate the control limits (where Z=3).

  12. p-Chart (Continued) 5. Plot the individual sample proportions, the average of the proportions, and the control limits

  13. An Example: Calculate sample means, sample ranges, mean of means, and mean of ranges.

  14. Control Limit Formulas Exhibit TN7.6

  15. x-Bar Chart

  16. R-Chart

  17. Matching Action to the Type of Variation • If you treat special causes like common causes, you lose an opportunity to track down and eliminate something specific that is increasing variation in your process. • If you treat common causes like special causes, you will most likely end up increasing variation (called “tampering”). • Taking the wrong action not only doesn’t improve the situation, it usually makes it worse.

  18. Quarterly Audit Scores Score · · · · · 1 2 3 4 5 Quarter

  19. Quarterly Audit Scores Score · · · · · 1 2 3 4 5 Quarter

  20. Quarterly Audit Scores Score · · · · · · · O · · · · · O · · · · · · · · O · · · · · · · · · · · O · · O 1 2 3 4 5

  21. Process Capability • Process limits (The “Voice of the Process” or The “Voice of the Data”) - based on natural (common cause) variation • Tolerance limits (The “Voice of the Customer”) – customer requirements • Process Capability – A measure of how “capable” the process is to meet customer requirements; compares process limits to tolerance limits

  22. (a) (b) specification specification natural variation natural variation (c) (d) specification specification natural variation natural variation Process Capability Evans and Lindsay The Management and Control of Quality, Southwestern Books.

  23. Process Capability Index, Cpk Capability Index - shows how well parts being produced fit into design limit specifications.

  24. Interpreting the Cpk Cpk < 1 Not Capable Cpk = 1 Capable at 3 Cpk = 1.33 Capable at 4 Cpk = 1.67 Capable at 5 Cpk = 2 Capable at 6

  25. Process Capability Index, Cpk Find the Cpk for the following: A process has a mean of 50.50 and a variance of 2.25. The product has a specification of 50.00 ± 4.00.

  26. Is 99% Good Enough? • 22,000 checks will be deducted from the wrong bank accounts in the next 60 minutes. • 20,000 incorrect drug prescriptions will be written in the next 12 months. • 12 babies will be given to the wrong parents each day.

  27. Motorola’s Initial Six SigmaMeasurement Process • Cycle time; e.g., 81 minutes  27 minutes  9 minutes  3 minutes  1 minute  20 seconds • Defects; e.g., 81 defects  27 defects  9 defects  3 defects 1 defect  0.3 defects REDUCE BOTH SIMULTANEOUSLY!

  28. Six Sigma Quality The objective of Six Sigma quality is 3.4 defects per million opportunities!

  29. 100K 10K 1K 100 10 1 2 3 4 5 6 7 But is Six Sigma Realistic? · IRS – Tax Advice (phone-in) · (66810 ppm) · · Restaurant Bills · Doctor Prescription Writing · Payroll Processing · · Average Company Order Write-up · Journal Vouchers Wire Transfers Air Line Baggage Handling · Defects Per Million Opportunities (DPMO) Purchased Material Lot Reject Rate (233 ppm) Best in Class Domestic Airline Flight Fatality Rate (3.4 ppm) (0.43 ppm) SIGMA

  30. A Partial List of Organizations in Atlanta Implementing Six Sigma • Coca-Cola • Home Depot • SunTrust Banks • Bank of America • Delta Airlines • Atlantic Envelope Company • GE Capital • Lithonia Lighting

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