1. Quality Assurance (Statistical Process Control) By Dr. Debadyuti Das

12. When to inspect Acceptance Sampling VS Process Control Process control is not feasible Process can be adjusted, stopped, inspected and started up again at a reasonable cost May be destructive or detrimental to the items Inspection not destructive or detrimental to the items Not very serious Consequences of passing on defectives are very high High Inspection cost per unit is low Acceptance Sampling Process Control

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

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

19. Control Chart 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 UCL LCL Sample number Mean Out of control Normal variation due to chance Abnormal variation due to assignable sources Abnormal variation due to assignable sources

20. Sampling Distribution Sampling distribution Process distribution Mean

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

25. Mean and Range Charts UCL LCL UCL LCL R-chart Detects shift Does not detect shift (process mean is shifting upward) Sampling Distribution x-Chart

26. Mean and Range Charts UCL Does not reveal increase UCL LCL LCL R-chart Reveals increase (process variability is increasing) Sampling Distribution x-Chart

30. Example of x-bar and R Charts: Required Data

31. Example of x-bar and R charts: Step 1. Calculate sample means, sample ranges, mean of means, and mean of ranges

32. Example of x-bar and R charts: Step 2. Determine Control Limit Formulas and Necessary Tabled Values

33. Example of x-bar and R charts: Steps 3&4. Calculate x-bar Chart and Plot Values UCL LCL

34. Example of x-bar and R charts: Steps 5&6. Calculate R-chart and Plot Values UCL LCL

35. Example of Constructing a p -Chart: Required Data Sample No. No. of Samples Number of defects found in each sample

36. Statistical Process Control Formulas: Attribute Measurements ( p -Chart) Given: Compute control limits:

37. Example of Constructing a p -chart: Step 1 1. Calculate the sample proportions, p (these are what can be plotted on the p -chart) for each sample

38. Example of Constructing a p -chart: Steps 2 & 3 2. Calculate the average of the sample proportions 3. Calculate the standard deviation of the sample proportion

39. Example of Constructing a p -chart: Step 4 4. Calculate the control limits UCL = 0.0924 LCL = -0.0204 (or 0)

40. Example of Constructing a p -Chart: Step 5 5. Plot the individual sample proportions, the average of the proportions, and the control limits UCL LCL

42. Process Capability C. Process variability exceeds specifications Lower Specification Upper Specification A. Process variability matches specifications Lower Specification Upper Specification B. Process variability well within specifications Lower Specification Upper Specification

43. Process Capability Ratio Process capability ratio, Cp = specification width process width Upper specification – lower specification 6  Cp =

44. Process Capability Index, C pk Shifts in Process Mean Capability Index shows how well parts being produced fit into design limit specifications. As a production process produces items in equipment or systems can cause differences in production performance from differing samples.