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Chapter 9A

Chapter 9A. Process Capability and SPC. 9A- 2. OBJECTIVES. Process Variation Process Capability Process Control Procedures Variable data Attribute data. 9A- 3. Basic Forms of Variation. Assignable variation is caused by factors that can be clearly identified and possibly managed.

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Chapter 9A

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  1. Chapter 9A Process Capability and SPC

  2. 9A-2 OBJECTIVES • Process Variation • Process Capability • Process Control Procedures • Variable data • Attribute data

  3. 9A-3 Basic Forms of Variation Assignable variationis caused by factors that can be clearly identified and possibly managed Example: A poorly trained employee that creates variation in finished product output. Common variationis inherent in the production process Example: A molding process that always leaves “burrs” or flaws on a molded item.

  4. 9A-4 High High Incremental Cost of Variability Incremental Cost of Variability Zero Zero Lower Spec Target Spec Upper Spec Lower Spec Target Spec Upper Spec Traditional View Taguchi’s View Taguchi’s View of Variation Traditional view is that quality within the LS and US is good and that the cost of quality outside this range is constant, where Taguchi views costs as increasing as variability increases, so seek to achieve zero defects and that will truly minimize quality costs.

  5. Process Capability • Process limits • Specification limits • How do the limits relate to one another?

  6. 9A-6 Process Capability Index, Cpk Capability Index shows how well parts being produced fit into design limit specifications. As a production process produces items small shifts in equipment or systems can cause differences in production performance from differing samples. Shifts in Process Mean

  7. 9A-7 Process Capability – A Standard Measure of How Good a Process Is. A simple ratio: Specification Width _________________________________________________________ Actual “Process Width” Generally, the bigger the better.

  8. 9A-8 Process Capability This is a “one-sided” Capability Index Concentration on the side which is closest to the specification - closest to being “bad”

  9. 9A-9 The Cereal Box Example • We are the maker of this cereal. Consumer reports has just published an article that shows that we frequently have less than 16 ounces of cereal in a box. • Let’s assume that the government says that we must be within ± 5 percent of the weight advertised on the box. • Upper Tolerance Limit = 16 + .05(16) = 16.8 ounces • Lower Tolerance Limit = 16 – .05(16) = 15.2 ounces • We go out and buy 1,000 boxes of cereal and find that they weight an average of 15.875 ounces with a standard deviation of .529 ounces.

  10. 9A-10 Cereal Box Process Capability • Specification or Tolerance Limits • Upper Spec = 16.8 oz • Lower Spec = 15.2 oz • Observed Weight • Mean = 15.875 oz • Std Dev = .529 oz

  11. 9A-11 What does a Cpk of .4253 mean? • An index that shows how well the units being produced fit within the specification limits. • This is a process that will produce a relatively high number of defects. • Many companies look for a Cpk of 1.3 or better… 6-Sigma company wants 2.0!

  12. 9A-12 Types of Statistical Sampling • Attribute (Go or no-go information) • Defectives refers to the acceptability of product across a range of characteristics. • Defects refers to the number of defects per unit which may be higher than the number of defectives. • p-chart application • Variable (Continuous) • Usually measured by the mean and the standard deviation. • X-bar and R chart applications

  13. Statistical Process Control (SPC) Charts 9A-13 UCL Normal Behavior LCL 1 2 3 4 5 6 Samples over time UCL Possible problem, investigate LCL 1 2 3 4 5 6 Samples over time UCL Possible problem, investigate LCL 1 2 3 4 5 6 Samples over time

  14. 9A-14 Control Limits are based on the Normal Curve x m z -3 -2 -1 0 1 2 3 Standard deviation units or “z” units.

  15. 9A-15 x Control Limits We establish the Upper Control Limits (UCL) and the Lower Control Limits (LCL) with plus or minus 3 standard deviations from some x-bar or mean value. Based on this we can expect 99.7% of our sample observations to fall within these limits. 99.7% LCL UCL

  16. 9A-16 Example of Constructing a p-Chart: Required Data Number of defects found in each sample Sample No. No. of Samples

  17. 9A-17 Statistical Process Control Formulas:Attribute Measurements (p-Chart) Given: Compute control limits:

  18. 9A-18 Example of Constructing a p-chart: Step 1 1. Calculate the sample proportions, p (these are what can be plotted on the p-chart) for each sample

  19. 9A-19 Example of Constructing a p-chart: Steps 2&3 2. Calculate the average of the sample proportions 3. Calculate the standard deviation of the sample proportion

  20. 9A-20 Example of Constructing a p-chart: Step 4 4. Calculate the control limits UCL = 0.0924 LCL = -0.0204 (or 0)

  21. 9A-21 UCL LCL Example of Constructing a p-Chart: Step 5 5. Plot the individual sample proportions, the average of the proportions, and the control limits

  22. 9A-22 Example of x-bar and R Charts: Required Data

  23. 9A-23 Example of x-bar and R charts: Step 1. Calculate sample means, sample ranges, mean of means, and mean of ranges.

  24. 9A-24 Example of x-bar and R charts: Step 2. Determine Control Limit Formulas and Necessary Tabled Values From Exhibit 9A.6

  25. 9A-26 UCL LCL Example of x-bar and R charts: Steps 3&4. Calculate x-bar Chart and Plot Values

  26. 9A-27 Example of x-bar and R charts: Steps 5&6. Calculate R-chart and Plot Values UCL LCL

  27. 9A-29 Question Bowl A methodology that is used to show how well parts being produced fit into a range specified by design limits is which of the following? • Capability index • Producer’s risk • Consumer’s risk • AQL • None of the above Answer: a. Capability index

  28. 9A-30 Question Bowl You want to prepare a p chart and you observe 200 samples with 10 in each, and find 5 defective units. What is the resulting “fraction defective”? • 25 • 2.5 • 0.0025 • 0.00025 • Can not be computed on data above Answer: c. 0.0025 (5/(2000x10)=0.0025)

  29. 9A-31 Question Bowl You want to prepare an x-bar chart. If the number of observations in a “subgroup” is 10, what is the appropriate “factor” used in the computation of the UCL and LCL? • 1.88 • 0.31 • 0.22 • 1.78 • None of the above Answer: b. 0.31

  30. 9A-32 Question Bowl You want to prepare an R chart. If the number of observations in a “subgroup” is 5, what is the appropriate “factor” used in the computation of the LCL? • 0 • 0.88 • 1.88 • 2.11 • None of the above Answer: a. 0

  31. 9A-33 Question Bowl You want to prepare an R chart. If the number of observations in a “subgroup” is 3, what is the appropriate “factor” used in the computation of the UCL? • 0.87 • 1.00 • 1.88 • 2.11 • None of the above Answer: e. None of the above

  32. 9A-34 End of Chapter 9A

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