1 / 70

Statistical Process Control

Statistical Process Control. Overview. Variation Control charts R charts X-bar charts P charts. Statistical Quality Control (SPC). Measures performance of a process Primary tool - statistics Involves collecting, organizing, & interpreting data Used to:

ainsley-odom
Download Presentation

Statistical Process Control

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related