Quality Assurance (Quality Control)

1. Quality Assurance(Quality Control)

2. Inspection before/after production Corrective action during production Quality built into the process Acceptance sampling Process control Continuous improvement The least progressive The most progressive Phases of Quality Assurance

3. Inputs Transformation Outputs Acceptance sampling Acceptance sampling Process control Inspection • How Much/How Often • Where/When • Centralized vs. On-site

4. Inspection Costs Cost Total Cost Cost of inspection Cost of passing defectives Optimal Amount of Inspection

5. Where to Inspect in the Process • Raw materials and purchased parts • Finished products • Before a costly operation • Before an irreversible process • Before a covering process

6. Examples of Inspection Points

7. Statistical Process Control • The Control Process • Define • Measure • Compare to a standard • Evaluate • Take corrective action • Evaluate corrective action

8. Statistical Process Control • Variations and Control • Random variation: Natural variations in the output of process, created by countless minor factors • Assignable variation: A variation whose source can be identified

9. Samplingdistribution Processdistribution Mean Sampling Distribution

10. -3s -2s +2s +3s Mean 95.5% 99.7% Normal Distribution s = Standard deviation

11. a/2 a/2 Mean LCL UCL a = Probabilityof Type I error Control Limits (Type I Error)

12. Samplingdistribution Processdistribution Mean Lowercontrollimit Uppercontrollimit Control Limits

13. Mean Charts • Two approaches: • If the process standard deviation (s) is available (x • If the process standard deviation is not available (use sample range to approximate the process variability)

14. Mean charts (SD of process available) • Upper control limit (UCL) • = average sample mean + z (S.D. of sample mean) • Lower control limit (LCL) • = average sample mean - z (S.D. of sample mean)

15. Mean charts (SD of process not available) • UCL = average of sample mean + A2 (average of sample range) • LCL = average of sample mean - A2 (average of sample range) • A2 is a parameter depending on the sample size and is obtainable from table.

16. Example • Means of sample taken from a process for making aluminum rods is 2 cm and the SD of the process is 0.1cm (assuming a normal distribution). Find the 3-sigma (99.7%) control limits assuming sample size of 16 are taken.

17. Example (solution) • x = SD of sample mean distribution • = SD of process / (sample size) • = 0.1 /  (16) = 0.025 • z = 3 • UCL = 2 + 3(0.025) = 2.075 • LCL = 2 - 0.075 = 1.925

18. Example(p.427) • Twenty samples of size 8 have been taken from a process. The average sample range of the 20 samples is 0.016cm and the average mean is 3cm. Determine the 3-sigma control limits.

19. Example • Average sample mean = 3cm • Average sample range = 0.016cm • Sample size = 8 • A2 = 0.37 (From Table 9-2) • UCL = 3 + 0.37(0.016) = 3.006 • LCL = 3 + 0.37(0.016) = 2.994

20. Control Chart Abnormal variationdue to assignable sources Out ofcontrol 1020 UCL 1010 1000 Mean Normal variationdue to chance 990 LCL 980 Abnormal variationdue to assignable sources 970 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Sample number

21. UCL LCL 1 2 3 4 Observations from Sample Distribution Sample number

22. UCL x-Chart LCL UCL LCL Mean and Range Charts Detects shift Does notdetect shift R-chart

23. UCL x-Chart LCL UCL R-chart Detects shift LCL Mean and Range Charts UCL LCL Does notdetect shift

24. Control Chart for Attributes • p-Chart - Control chart used to monitor the proportion of defectives in a process • c-Chart - Control chart used to monitor the number of defects per unit

25. Use of p-Charts • When observations can be placed into two categories. • Good or bad • Pass or fail • Operate or do not operate • When the data consists of multiple samples of several observations each

26. p-chart • The center line is the average fraction (defective) p in the population if p is known, or it can be estimated from samples is it is unknown. • p = SD of sample distribution • = {p(1-p)/n} • UCLp = p + zp • LCLp = p - zp

27. Example (p.431) • The following table indicates the defective items in 20 samples, each of size 100. Construct a control chart that will describe 95.5% of the chance variations of the process

28. The following table indicates the defective items in 20 samples, each of size 100. Construct a control chart that will describe 95.5% of the chance variations of the process No. of defective items Example

29. Example (solution) • Population mean not available, to be estimated from sample mean • Total No. of defective items = 220 • Estimate sample mean = 220/{20(100)}=.11 • SD of sample = {.11(1-.11)/100}= 0.03 • z = 2 (2-sigma) • UCLp = .11 + 2(.03) = 0.17 • LCLp = .11 - 2(.03) = 0.05 • Thus a control chart can be plotted (p.431)

30. Use of c-Charts • Use only when the number of occurrences per unit of measure can be counted; nonoccurrences cannot be counted. • Scratches, chips, dents, or errors per item • Cracks or faults per unit of distance • Calls, complaints, failures per unit of time

31. LowerSpecification UpperSpecification Process variabilitymatches specifications LowerSpecification UpperSpecification Process variabilitywell within specifications LowerSpecification UpperSpecification Process variabilityexceeds specifications Process Capability