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Statistical Process Control

Statistical Process Control. A. A. Elimam. Two Primary Topics in Statistical Quality Control. Statistical process control (SPC) is a statistical method using control charts to check a production process - prevent poor quality. In TQM all workers are trained in SPC methods.

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Statistical Process Control

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  1. Statistical ProcessControl A. A. Elimam

  2. Two Primary Topics in Statistical Quality Control • Statistical process control (SPC) is a statistical method using control charts to check a production process - prevent poor quality. In TQM all workers are trained in SPC methods.

  3. Two Primary Topics in Statistical Quality Control • Acceptance Sampling involves inspecting a sample of product. If sample fails reject the entire product - identifies the products to throw away or rework. Contradicts the philosophy of TQM. Why ?

  4. Inspection • Traditional Role: at the beginning and end of the production process • Relieves Operator from the responsibility of detecting defectives & quality problems • It was the inspection's job • In TQM, inspection is part of the process & it is the operator’s job • Customers may require independent inspections

  5. How Much to Inspect? • Complete or 100 % Inspection. • Viable for products that can cause safety problems • Does not guarantee catching all defectives • Too expensive for most cases • Inspection by Sampling • Sample size : representative • A must in destructive testing (e.g... Tasting food)

  6. Where To Inspect ? • In TQM , inspection occurs throughout the production process • IN TQM, the operator is the inspector • Locate inspection where it has the most effect (e.g.... prior to costly or irreversible operation) • Early detection avoids waste of more resources

  7. Destructive Testing Product cannot be used after testing (e.g.. taste or breaking item) Sample testing Could be costly Non-Destructive Testing Product is usable after testing 100% or sampling Quality Testing

  8. Quality Measures:Attributes • Attribute is a qualitative measure • Product characteristics such as color, taste, smell or surface texture • Simple and can be evaluated with a discrete response (good/bad, yes/no) • Large sample size (100’s)

  9. Quality Measures:Variables • A quantitative measure of a product characteristic such as weight, length, etc. • Small sample size (2-20) • Requires skilled workers

  10. Variation & Process Control Charts • Variation always exists • Two Types of Variation • Causal: can be attributed to a cause. If we know the cause we can eliminate it. • Random: Cannot be explained by a cause. An act of nature - need to accept it. • Process control charts are designed to detect causal variations

  11. Control Charts: Definition & Types • A control chart is a graph that builds the control limits of a process • Control limits are the upper and lower bands of a control chart • Types of Charts: • Measurement by Variables: X-bar and R charts • Measurement by Attributes: p and c

  12. Process Control Chart & Control Criteria 1. No sample points outside control limits. 2. Most points near the process average. 3. Approximately equal No. of points above & below center. 4. Points appear to be randomly distributed around the center line. 5. No extreme jumps. 6. Cannot detect trend.

  13. Basis of Control Charts • Specification Control Charts • Target Specification: Process Average • Tolerances define the specified upper and lower control limits • Used for new products (historical measurements are not available) • Historical Data Control Charts • Process Average, upper & lower control limits: based on historical measurements • Often used in well established processes

  14. Common Causes 425 Grams

  15. Assignable Causes Average Grams (a) Location

  16. Assignable Causes Average Grams (b) Spread

  17. Assignable Causes Average Grams (b) Spread

  18. Assignable Causes Average Grams (c) Shape

  19. Effects of Assignable Causes on Process Control Assignable causes present

  20. Effects of Assignable Causes on Process Control No assignable causes

  21. Sample Means and the Process Distribution Mean Distribution of sample means Process distribution 425 Grams

  22. The Normal Distribution Mean -3 -2 -1 +1 +2 +3 68.26% 95.44% 99.97%  = Standard deviation

  23. Control Charts Assignable causes likely UCL Nominal LCL 1 2 3 Samples

  24. Using Control Charts for Process Improvement • Measure the process • When problems are indicated, find the assignable cause • Eliminate problems, incorporate improvements • Repeat the cycle

  25. Control Chart Examples UCL Nominal Variations LCL Sample number (a)

  26. Control Chart Examples UCL Nominal Variations LCL Sample number (b)

  27. Control Chart Examples UCL Nominal Variations LCL Sample number (c)

  28. Control Chart Examples UCL Nominal Variations LCL Sample number (d)

  29. Control Chart Examples UCL Nominal Variations LCL Sample number (e)

  30. The Normal Distribution • Measures of Variability: • Most accurate measure •  = Standard Deviation • Approximate Measure - Simpler to compute • R = Range • Range is less accurate as the sample size • gets larger • Average  = Average R when n = 2

  31. Control Limits and Errors Type I error: Probability of searching for a cause when none exists UCL Process average LCL (a) Three-sigma limits

  32. Control Limits and Errors Type I error: Probability of searching for a cause when none exists UCL Process average LCL (b) Two-sigma limits

  33. Control Limits and Errors Type II error: Probability of concluding that nothing has changed UCL Shift in process average Process average LCL (a) Three-sigma limits

  34. Control Limits and Errors Type II error: Probability of concluding that nothing has changed UCL Shift in process average Process average LCL (b) Two-sigma limits

  35. Control Charts for Variables Mandara Industries

  36. Control Charts for Variables Special Metal Screw Sample Sample Number 1 2 3 4 Range Mean 1 0.5014 0.5022 0.5009 0.5027 2 0.5021 0.5041 0.5032 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

  37. Control Charts for Variables Special Metal Screw Sample Sample Number 1 2 3 4 Range Mean 1 0.5014 0.5022 0.5009 0.5027 2 0.5021 0.5041 0.5032 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

  38. Control Charts for Variables Special Metal Screw Sample Sample Number 1 2 3 4 Range Mean 1 0.5014 0.5022 0.5009 0.5027 0.0018 2 0.5021 0.5041 0.5032 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

  39. Control Charts for Variables Special Metal Screw Sample Sample Number 1 2 3 4 Range Mean 1 0.5014 0.5022 0.5009 0.5027 0.0018 0.5018 2 0.5021 0.5041 0.5032 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 (0.5014 + 0.5022 + 0.5009 + 0.5027)/4 = 0.5018

  40. Control Charts for Variables Special Metal Screw Sample Sample Number 1 2 3 4 Range Mean 1 0.5014 0.5022 0.5009 0.5027 0.0018 0.5018 2 0.5021 0.5041 0.5032 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 (0.5014 + 0.5022 + 0.5009 + 0.5027)/4 = 0.5018

  41. Control Charts for Variables Special Metal Screw Sample Sample Number 1 2 3 4 Range Mean 1 0.5014 0.5022 0.5009 0.5027 0.0018 0.5018 2 0.5021 0.5041 0.5032 0.5020 0.0021 0.5029 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 0.5039 0.0022 0.5043 R = 0.0020 x = 0.5025

  42. Control Charts for Variables R = 0.0020 UCLR = D4R LCLR = D3R Control Charts - Special Metal Screw R - Charts

  43. 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

  44. Control Charts for Variables R = 0.0020 D4= 2.282 D3 = 0 UCLR = D4R LCLR = D3R Control Charts - Special Metal Screw R - Charts UCLR = 2.282 (0.0020) = 0.00456 in. LCLR = 0 (0.0020) = 0 in.

  45. Range Chart - Special Metal Screw R = 0.0020 0.005 0.004 0.003 0.002 0.001 0 UCLR = 0.00456 Range (in.) LCLR = 0 1 2 3 4 5 6 Sample number

  46. Control Charts for Variables 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 40.729 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 - Special Metal Screw

  47. Control Charts for Variables x - Charts R = 0.0020 A2 = 0.729 x = 0.5025 UCLx = x + A2R LCLx = x - A2R UCLx = 0.5025 + 0.729 (0.0020) = 0.5040 in. Control Charts - Special Metal Screw

  48. Control Charts for Variables x - Charts R = 0.0020 A2 = 0.729 x = 0.5025 UCLx = x + A2R LCLx = x - A2R UCLx = 0.5025 + 0.729 (0.0020) = 0.5040 in. LCLx = 0.5025 - 0.729 (0.0020) = 0.5010 in. Control Charts - Special Metal Screw

  49. UCLx = 0.5040 x = 0.5025 LCLx = 0.5010 Average Chart - Special Metal Screw 0.5050 0.5040 0.5030 0.5020 0.5010 Average (in.) 1 2 3 4 5 6 Sample number

  50. UCLx = 0.5040 x = 0.5025 LCLx = 0.5010 1 2 3 4 5 6 Sample number Average Chart - Special Metal Screw 0.5050 0.5040 0.5030 0.5020 0.5010 • Measure the process • Find the assignable cause • Eliminate the problem • Repeat the cycle Average (in.)

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