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INT 506/706: Total Quality Management

INT 506/706: Total Quality Management. Lec #6, Process Capability. Outline. Individual values vs. averages Control limits vs. Specs 6 σ spread versus specs Calculating Process Capability Indices. Process Capability. Individual vs. averages. Individual vs. averages.

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INT 506/706: Total Quality Management

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  1. INT 506/706: Total Quality Management Lec #6, Process Capability

  2. Outline • Individual values vs. averages • Control limits vs. Specs • 6σ spread versus specs • Calculating Process Capability Indices

  3. Process Capability

  4. Individual vs. averages

  5. Individual vs. averages The ability of X-bar to approximate μ is measured by the following equation:

  6. Individual vs. averages IF the process can be assumed to be normal, the population standard deviation can be estimated from either the sample standard deviation (s) or the range (R).

  7. Control limits vs Specifications A process under control exhibits: • 2/3 of points near center • Few points close to the center • Points around centerline • Points balanced on both sides • No points beyond control limits • No patterns or trends

  8. Control limits vs Specifications

  9. 6σ Spread versus Specs 3 Possible CASES 6σ < USL – LSL 6σ = USL – LSL 6σ > USL - LSL

  10. CASE #1 6σ < USL – LSL

  11. CASE #2 6σ = USL – LSL

  12. CASE #3 6σ > USL – LSL

  13. Calculating 6σ Assuming process is STABLE and IN CONTROL • 20 subgroups of n=4 • Calculate sample std dev, si, for each sample • Calculate average sample std dev, • Calculate pop std dev • Multiply pop std dev *6

  14. Example

  15. Example

  16. Capability Index Cp

  17. Capability Index Cp EXAMPLE INTERPRETATION: Process NOT capable (case 3)

  18. Capability Ratio, Cr Inverse of Cp so larger the ratio, the LESS capable the process is of meeting specifications

  19. Cpk Cp and Cr do not take into account the centering of the process Where Z(min)=

  20. Cpk

  21. Cpk

  22. Review • Review pdf file in blackboard • “CapabilityCaseStudy” • Put into Minitab and run capability modules to see what you come up with • Is it the same as the case study? • Do you understand the interpretation of the case study?

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