Statistical Process Control

# Statistical Process Control

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## Statistical Process Control

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1. Statistical Process Control

2. Overview • Variation • Control charts • R charts • X-bar charts • P charts

3. Statistical Quality Control (SPC) • Measures performance of a process • Primary tool - statistics • Involves collecting, organizing, & interpreting data • Used to: • Control the process as products are produced • Inspect samples of finished products

4. Bottling Company • Machine automatically fills a 20 oz bottle. • Problem with filling too much? Problems with filling to little? • So Monday the average is 20.2 ounces. • Tuesday the average is 19.6 ounces. • Is this normal? Do we need to be concerned? • Wed is 19.4 ounces.

5. Natural Variation • Machine can not fill every bottle exactly the same amount – close but not exactly.

6. Assignable variation • A cause for part of the variation

7. SPC • Objective: provide statistical signal when assignable causes of variation are present

8. Control Chart Types Continuous Numerical Data Categorical or Discrete Numerical Data Control Charts Variables Attributes Charts Charts R P C X Chart Chart Chart Chart

9. Measuring quality Attributes • Characteristics for which you focus on defects • Classify products as either ‘good’ or ‘bad’, or count # defects • e.g., radio works or not • Categorical or discrete random variables Variables • Characteristics that you measure, e.g., weight, length • May be in whole or in fractional numbers • Continuous random variables

10. Control Chart Purposes • Show changes in data pattern • e.g., trends • Make corrections before process is out of control • Show causes of changes in data • Assignable causes • Data outside control limits or trend in data • Natural causes • Random variations around average

11. Figure S6.7

12. Steps to Follow When Using Control Charts TO SET CONTROL CHART LIMITS • Collect 20-25 samples of n=4 or n=5 a stable process • compute the mean of each sample. • Calculate control limits • Compute the overall means • Calculate the upper and lower control limits.

13. Steps to Follow When Using Control Charts - continued TO MONITOR PROCESS USING THE CONTROL CHARTS: • Collect and graph data • Graph the sample means and ranges on their respective control charts • Determine whether they fall outside the acceptable limits. • Investigate points or patterns that indicate the process is out of control. Assign causes for the variations. • Collect additional samples and revalidate the control limits.

14. R Chart • Monitors variability in process • Variables control chart • Interval or ratio scaled numerical data • Shows sample ranges over time • Difference between smallest & largest values in inspection sample

15. R Chart Control Limits From Table S6.1 Sample Range at Time i # Samples

16. Control Charts for Variables West Allis Industries The management of West Allis Industries is concerned about the production of a special metal screw ordered by several of their largest customers. The diameter of the screw is critical.

17. Control Charts for Variables Special Metal Screw Sample Sample Number 1 2 3 4 1 2 3 4 5

18. Control Charts for Variables Special Metal Screw Sample Sample Number 1 2 3 4 1 0.5014 0.5022 0.5009 0.5027 2 0.5021 0.5041 0.5024 0.5020 3 0.5018 0.5026 0.5035 0.5023 4 0.5008 0.5034 0.5024 0.5015 5 0.5041 0.5056 0.5034 0.5047 Should be at least 20 samples of size 4 to calculate the control limits.

19. Control Charts for Variables Special Metal Screw Sample Sample Number 1 2 3 4 R 1 0.5014 0.5022 0.5009 0.5027 2 0.5021 0.5041 0.5024 0.5020 3 0.5018 0.5026 0.5035 0.5023 4 0.5008 0.5034 0.5024 0.5015 5 0.5041 0.5056 0.5034 0.5039

20. Control Charts for Variables Special Metal Screw Sample Sample Number 1 2 3 4 R 1 0.5014 0.5022 0.5009 0.5027 2 0.5021 0.5041 0.5024 0.5020 3 0.5018 0.5026 0.5035 0.5023 4 0.5008 0.5034 0.5024 0.5015 5 0.5041 0.5056 0.5034 0.5039

21. Control Charts for Variables Special Metal Screw Sample Sample Number 1 2 3 4 R 1 0.5014 0.5022 0.5009 0.5027 2 0.5021 0.5041 0.5024 0.5020 3 0.5018 0.5026 0.5035 0.5023 4 0.5008 0.5034 0.5024 0.5015 5 0.5041 0.5056 0.5034 0.5039 0.5027 – 0.5009 = 0.0018

22. Control Charts for Variables Special Metal Screw Sample Sample Number 1 2 3 4 R 1 0.5014 0.5022 0.5009 0.5027 0.0018 2 0.5021 0.5041 0.5024 0.5020 3 0.5018 0.5026 0.5035 0.5023 4 0.5008 0.5034 0.5024 0.5015 5 0.5041 0.5056 0.5034 0.5039 0.5027 – 0.5009 = 0.0018

23. Control Charts for Variables Special Metal Screw Sample Sample Number 1 2 3 4 R 1 0.5014 0.5022 0.5009 0.5027 0.0018 2 0.5021 0.5041 0.5024 0.5020 3 0.5018 0.5026 0.5035 0.5023 4 0.5008 0.5034 0.5024 0.5015 5 0.5041 0.5056 0.5034 0.5039 0.5027 – 0.5009 = 0.0018 0.5041 - 0.5020 = 0.0021

24. Control Charts for Variables Special Metal Screw Sample Sample Number 1 2 3 4 R 1 0.5014 0.5022 0.5009 0.5027 0.0018 2 0.5021 0.5041 0.5024 0.5020 0.0021 3 0.5018 0.5026 0.5035 0.5023 0.0017 4 0.5008 0.5034 0.5024 0.5015 0.0026 5 0.5041 0.5056 0.5034 0.5047 0.0022

25. Control Charts for Variables Special Metal Screw Sample Sample Number 1 2 3 4 R 1 0.5014 0.5022 0.5009 0.5027 0.0018 2 0.5021 0.5041 0.5024 0.5020 0.0021 3 0.5018 0.5026 0.5035 0.5023 0.0017 4 0.5008 0.5034 0.5024 0.5015 0.0026 5 0.5041 0.5056 0.5034 0.5047 0.0022 R = 0.0021

26. R = 0.0021 UCLR = D4R LCLR = D3R Control Charts for Variables Control Charts – Special Metal Screw R-Charts

27. Control Chart Factors Factor for UCL Factor for Factor Size of and LCL for LCL for UCL for Sample x-Charts R-Charts R-Charts (n) (A2) (D3) (D4) 2 1.880 0 3.267 3 1.023 0 2.575 4 0.729 0 2.282 5 0.577 0 2.115 6 0.483 0 2.004 7 0.419 0.076 1.924 Control Charts for Variables

28. Control Chart Factors Factor for UCL Factor for Factor Size of and LCL for LCL for UCL for Sample x-Charts R-Charts R-Charts (n) (A2) (D3) (D4) 2 1.880 0 3.267 3 1.023 0 2.575 4 0.729 0 2.282 5 0.577 0 2.115 6 0.483 0 2.004 7 0.419 0.076 1.924 R = 0.0020 D4 = 2.2080 Control Charts for Variables Control Charts - Special Metal Screw R - Charts

29. R = 0.0021 D4 = 2.282 D3 = 0 UCLR = D4R LCLR = D3R Control Charts for Variables Control Charts—Special Metal Screw R-Charts

30. R = 0.0021 D4= 2.282 D3 = 0 UCLR = D4R LCLR = D3R Control Charts for Variables Control Charts—Special Metal Screw R-Charts UCLR = 2.282 (0.0021) = 0.00479 in.

31. R = 0.0021 D4= 2.282 D3 = 0 UCLR = D4R LCLR = D3R Control Charts for Variables Control Charts—Special Metal Screw R-Charts UCLR = 2.282 (0.0021) = 0.00479 in. LCLR = 0 (0.0021) = 0 in.

32. R = 0.0021 D4= 2.282 D3 = 0 UCLR = D4R LCLR = D3R Control Charts for Variables Control Charts—Special Metal Screw R-Charts UCLR = 2.282 (0.0021) = 0.00479 in. LCLR = 0 (0.0021) = 0 in.

33. Range Chart - Special Metal Screw

34. X Chart • Monitors process average • Variables control chart • Interval or ratio scaled numerical data • Shows sample means over time

35. X Chart Control Limits From Table S6.1 Sample Range at Time i Sample Mean at Time i # Samples

36. Control Charts for Variables Special Metal Screw Sample Sample Number 1 2 3 4 1 0.5014 0.5022 0.5009 0.5027 2 0.5021 0.5041 0.5024 0.5020 3 0.5018 0.5026 0.5035 0.5023 4 0.5008 0.5034 0.5024 0.5015 5 0.5041 0.5056 0.5034 0.5047

37. Control Charts for Variables Special Metal Screw Sample Sample Number 1 2 3 4 Rx 1 0.5014 0.5022 0.5009 0.5027 2 0.5021 0.5041 0.5024 0.5020 3 0.5018 0.5026 0.5035 0.5023 4 0.5008 0.5034 0.5024 0.5015 5 0.5041 0.5056 0.5034 0.5039 _

38. Control Charts for Variables Special Metal Screw Sample Sample Number 1 2 3 4 Rx 1 0.5014 0.5022 0.5009 0.5027 2 0.5021 0.5041 0.5024 0.5020 3 0.5018 0.5026 0.5035 0.5023 4 0.5008 0.5034 0.5024 0.5015 5 0.5041 0.5056 0.5034 0.5039 _

39. Control Charts for Variables Special Metal Screw Sample Sample Number 1 2 3 4 Rx 1 0.5014 0.5022 0.5009 0.5027 0.0018 0.5018 2 0.5021 0.5041 0.5024 0.5020 3 0.5018 0.5026 0.5035 0.5023 4 0.5008 0.5034 0.5024 0.5015 5 0.5041 0.5056 0.5034 0.5039 _ (0.5014 + 0.5022 + 0.5009 + 0.5027)/4 = 0.5018

40. Control Charts for Variables Special Metal Screw Sample Sample Number 1 2 3 4 Rx 1 0.5014 0.5022 0.5009 0.5027 0.0018 0.5018 2 0.5021 0.5041 0.5024 0.5020 3 0.5018 0.5026 0.5035 0.5023 4 0.5008 0.5034 0.5024 0.5015 5 0.5041 0.5056 0.5034 0.5039 _ (0.5021 + 0.5041 + 0.5024 + 0.5020)/4 = 0.5027

41. Control Charts for Variables Special Metal Screw Sample Sample Number 1 2 3 4 Rx 1 0.5014 0.5022 0.5009 0.5027 0.0018 0.5018 2 0.5021 0.5041 0.5024 0.5020 0.0021 0.5027 3 0.5018 0.5026 0.5035 0.5023 0.0017 0.5026 4 0.5008 0.5034 0.5024 0.5015 0.0026 0.5020 5 0.5041 0.5056 0.5034 0.5047 0.0022 0.5045 _

42. Control Charts for Variables Special Metal Screw Sample Sample Number 1 2 3 4 Rx 1 0.5014 0.5022 0.5009 0.5027 0.0018 0.5018 2 0.5021 0.5041 0.5024 0.5020 0.0021 0.5027 3 0.5018 0.5026 0.5035 0.5023 0.0017 0.5026 4 0.5008 0.5034 0.5024 0.5015 0.0026 0.5020 5 0.5041 0.5056 0.5034 0.5047 0.0022 0.5045 R = 0.0021 x = 0.5027 _ =

43. X-Charts R = 0.0021 x = 0.5027 = = UCLx = x + A2R LCLx = x - A2R = Control Charts for Variables Control Charts—Special Metal Screw Example 7.1

44. Control Chart Factors Factor for UCL Factor for Factor Size of and LCL for LCL for UCL for Sample x-Charts R-Charts R-Charts (n) (A2) (D3) (D4) 2 1.880 0 3.267 3 1.023 0 2.575 4 0.729 0 2.282 5 0.577 0 2.115 6 0.483 0 2.004 7 0.419 0.076 1.924 x - Charts R = 0.0020 x = 0.5025 UCLx = x + A2R LCLx = x - A2R Control Charts for Variables Control Charts - Special Metal Screw Example 7.1

45. x- Charts R = 0.0021 A2 = 0.729 x = 0.5027 = = UCLx = x + A2R LCLx = x - A2R = Control Charts for Variables Control Charts—Special Metal Screw

46. x-Charts R = 0.0021 A2 = 0.729 x = 0.5027 = = UCLx = x + A2R LCLx = x - A2R = UCLx = 0.5027 + 0.729 (0.0021) = 0.5042 in. Control Charts for Variables Control Charts—Special Metal Screw Example 7.1

47. x-Charts R = 0.0021 A2 = 0.729 x = 0.5027 = = UCLx = x + A2R LCLx = x - A2R = UCLx = 0.5027 + 0.729 (0.0021) = 0.5042 in. LCLx = 0.5027 – 0.729 (0.0021) = 0.5012 in. Control Charts for Variables Control Charts—Special Metal Screw

48. x-Chart Special Metal Screw

49. x-Chart Special Metal Screw

50. Investigate Cause x-Chart Special Metal Screw