Statistical Process Control

1. Statistical Process Control Douglas M. Stewart, Ph.D. The Anderson Schools of Management The University of New Mexico

2. Quality Control (QC) • Control – the activity of ensuring conformance to requirements and taking corrective action when necessary to correct problems • Importance • Daily management of processes • Prerequisite to longer-term improvements

3. Designing the QC System • Quality Policy and Quality Manual • Contract management, design control and purchasing • Process control, inspection and testing • Corrective action and continual improvement • Controlling inspection, measuring and test equipment (metrology, measurement system analysis and calibration) • Records, documentation and audits

4. Example of QC: HACCP System • Hazard analysis • Critical control points • Preventive measures with critical limits for each control point • Procedures to monitor the critical control points • Corrective actions when critical limits are not met • Verification procedures • Effective record keeping and documentation

5. Inspection/Testing Points • Receiving inspection • In-process inspection • Final inspection

6. Receiving Inspection • Spot check procedures • 100 percent inspection • Acceptance sampling

7. 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 Acceptance Sampling

8. Arguments for: Provides an assessment of risk Inexpensive and suited for destructive testing Requires less time than other approaches Requires less handling Reduces inspector fatigue Arguments against: Does not make sense for stable processes Only detects poor quality; does not help to prevent it Is non-value-added Does not help suppliers improve Pros and Cons of Acceptance Sampling

9. In-Process Inspection • What to inspect? • Key quality characteristics that are related to cost or quality (customer requirements) • Where to inspect? • Key processes, especially high-cost and value-added • How much to inspect? • All, nothing, or a sample

10. Economic Model C1 = cost of inspection and removal of nonconforming item C2 = cost of repair p = true fraction nonconforming Breakeven Analysis: p*C2 = C1 If p > C1 / C2 , use 100% inspection If p < C1 / C2 , do nothing

11. Human Factors in Inspection complexity defect rate repeated inspections inspection rate Inspection should never be a means of assuring quality. The purpose of inspection should be to gather information to understand and improve the processes that produce products and services.

12. Gauges and Measuring Instruments • Variable gauges • Fixed gauges • Coordinate measuring machine • Vision systems

13. Examples of Gauges

14. Metrology - Science of Measurement Accuracy - closeness of agreement between an observed value and a standard Precision - closeness of agreement between randomly selected individual measurements

15. Repeatability and Reproducibility • Repeatability (equipment variation) – variation in multiple measurements by an individual using the same instrument. • Reproducibility (operator variation) - variation in the same measuring instrument used by different individuals

16. Repeatability and Reproducibility Studies • Quantify and evaluate the capability of a measurement system • Select m operators and n parts • Calibrate the measuring instrument • Randomly measure each part by each operator for r trials • Compute key statistics to quantify repeatability and reproducibility

17. Reliability and Reproducibility Studies(2)

18. Reliability and Reproducibility Studies(3)

19. R&R Constants

20. R&R Evaluation • Under 10% error - OK • 10-30% error - may be OK • over 30% error - unacceptable

21. R&R Example • R&R Study is to be conducted on a gauge being used to measure the thickness of a gasket having specification of 0.50 to 1.00 mm. We have three operators, each taking measurement on 10 parts in 2 separate trials.

23. Calibration • Calibration - comparing a measurement device or system to one having a known relationship to national standards • Traceability to national standards maintained by NIST, National Institute of Standards and Technology

24. Statistical Process Control (SPC) • A methodology for monitoring a process to identify special causes of variation and signal the need to take corrective action when appropriate • SPC relies on control charts

25. Common Causes Special Causes

26. Histograms do not take into account changes over time. Control charts can tell us when a process changes

27. Control Chart Applications • Establish state of statistical control • Monitor a process and signal when it goes out of control • Determine process capability

28. Commonly Used Control Charts • Variables data • x-bar and R-charts • x-bar and s-charts • Charts for individuals (x-charts) • Attribute data • For “defectives” (p-chart, np-chart) • For “defects” (c-chart, u-chart)

29. Developing Control Charts • Prepare • Choose measurement • Determine how to collect data, sample size, and frequency of sampling • Set up an initial control chart • Collect Data • Record data • Calculate appropriate statistics • Plot statistics on chart

31. Next Steps • Determine trial control limits • Center line (process average) • Compute UCL, LCL • Analyze and interpret results • Determine if in control • Eliminate out-of-control points • Recompute control limits as necessary

36. Typical Out-of-Control Patterns • Point outside control limits • Sudden shift in process average • Cycles • Trends • Hugging the center line • Hugging the control limits • Instability

37. Shift in Process Average

38. Identifying Potential Shifts

39. Cycles

40. Trend

41. Final Steps • Use as a problem-solving tool • Continue to collect and plot data • Take corrective action when necessary • Compute process capability

42. Process Capability • Capability Indices

43. Process Capability (2)

44. Control In Control Out of Control Capability Capable Not Capable IDEAL Capability Versus Control

45. Process Capability Calculations

46. Excel Template

48. Special Variables Control Charts • x-bar and s charts • x-chart for individuals