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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 • 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 Attributes 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. Control Charts for Variables Glacier Bottling • Management at Glacier Bottling is concerned about their filling process. In particular, they want to know whether or not the machines are really filling the bottles with 16 ounces. • Create an Xbar chart that will be used to monitor the process. • Collected data for 25 days. Each day, pulled 4 bottles from the filling line and measured the amount in the bottle.

  15. Glacier Bottling Remember: There are 25 samples of size 4 to calculate the control limits. We are doing the first 5 right now…

  16. Setting Control Limits for R chart

  17. 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

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

  19. Glacier Bottling 16.02 – 15.83 = 0.19

  20. Glacier Bottling 16.02 – 15.83 = 0.19 16.12 – 15.85 = 0.27

  21. Rbar = 0.29 ounce

  22. R = 0.29 UCLR = D4R LCLR = D3R Glacier Bottling R-Charts

  23. 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 This chart is in your text and will be provided for exams if needed.

  24. R = 0.29 UCLR = D4R LCLR = D3R Glacier Bottling R-Charts D4 = 2.282 D3 = 0 UCLR = 2.282 (0.29) = 0.654 ounce LCLR = 0(0.29) = 0 ounce

  25. R = 0.29 UCLR = D4R LCLR = D3R Glacier Bottling R-Charts D4 = 2.282 D3 = 0 UCLR = 2.282 (0.29) = 0.654 ounce LCLR = 0(0.29) = 0 ounce

  26. SETUP CHARTS Glacier Bottling

  27. MONITORING Glacier Bottling

  28. Figure S6.7

  29. Glacier Bottling

  30. Figure S6.7

  31. Glacier Bottling

  32. Figure S6.7

  33. Glacier Bottling

  34. Figure S6.7

  35. Glacier Bottling

  36. Figure S6.7

  37. Setting Control Limits for Xbar chart

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

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

  40. Glacier Bottling (15.85+16.02+15.83+15.93)/4 = 15.908

  41. Glacier Bottling (16.12+16.00+15.85+16.01)/4 = 15.995

  42. RBar = 0.29 ounce XBarBar = 15.9469 ounces

  43. Rbar = 0.29 xbarbar = 15.9469 Glacier Bottling:Setting Control Limits for XBar chart Xbar –Chart UCLx = x + A2R LCLx = x - A2R

  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 This chart is in your text and will be provided for exams if needed.

  45. R = 0.29 x = 15.9469 A2 = 0.729 UCLx = 15.9469 + 0.729 (0.29) = 16.156 oz. Glacier Bottling:Setting Control Limits for XBar chart X –Chart = UCLx = x + A2R LCLx = x - A2R = =

  46. R = 0.29 x = 15.9469 A2 = 0.729 UCLx = 15.9469 + 0.729 (0.29) = 16.156 oz. LCLx = 15.9469 – 0.729 (0.29) = 15.738 oz. Glacier Bottling:Setting Control Limits for XBar chart X –Chart = UCLx = x + A2R LCLx = x - A2R = =

  47. Glacier Bottling