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Technical Note 8 Process Capability and Statistical Quality Control

Technical Note 8 Process Capability and Statistical Quality Control. Process Variation Process Control Procedures Attribute data Variable data Process Capability Acceptance Sampling. Basic Causes of Variation. Assignable causes Common causes Key : .

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Technical Note 8 Process Capability and Statistical Quality Control

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  1. Technical Note 8Process Capability and Statistical Quality Control • Process Variation • Process Control Procedures • Attribute data • Variable data • Process Capability • Acceptance Sampling

  2. Basic Causes of Variation • Assignable causes • Common causes • Key:

  3. Types of Statistical Quality Control Statistical Statistical Quality Control Quality Control Process Acceptance Process Acceptance Control Sampling Control Sampling Variables Attributes Variables Attributes Variables Attributes Variables Attributes Charts Charts Charts Charts

  4. Types of Control Charts • Attribute (Go or no-go information) • Defectives • p-chart application • Variable (Continuous) • Usually measured by the mean and the standard deviation. • X-bar and R chart applications

  5. x LCL UCL Control Limits We establish the Upper Control Limits (UCL) and the Lower Control Limits (LCL) with plus or minus 3 standard deviations. Based on this we can expect 99.7% of our sample observations to fall within these limits. 99.7%

  6. Statistical Process Control (SPC) Charts UCL LCL 1 2 3 4 5 6 Samples over time UCL LCL 1 2 3 4 5 6 Samples over time UCL LCL 1 2 3 4 5 6 Samples over time Excellent review in exhibit TN8.5.

  7. Number of defectives Sample size Sample Example of Constructing a p-Chart: Required Data

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

  9. 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.

  10. 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

  11. Example of Constructing a p-chart: Step 4 4. Calculate the control limits.

  12. Example of Constructing a p-Chart: Step 5 5. Plot the individual sample proportions, the average of the proportions, and the control limits

  13. R Chart • Type of variables control chart • Shows sample ranges over time • Monitors variability in process • Example: Weigh samples of coffee & compute ranges of samples; Plot

  14. Sample Range in sample i From Table (function of sample size) # Samples R Chart Control Limits

  15. R Chart Example You’re manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For 7 days, you collect data on 5 deliveries per day. Is the process in control?

  16. R Chart Hotel Data Sample DayDelivery TimeMean Range 1 7.30 4.20 6.10 3.45 5.55

  17. R Chart Hotel Data Sample DayDelivery TimeMean Range 1 7.30 4.20 6.10 3.45 5.55 5.32 3.85 2 4.60 8.70 7.60 4.43 7.62 6.59 4.27 3 5.98 2.92 6.20 4.20 5.10 4.88 3.28 4 7.20 5.10 5.19 6.80 4.21 5.70 2.99 5 4.00 4.50 5.50 1.89 4.46 4.07 3.61 6 10.10 8.10 6.50 5.06 6.94 7.34 5.04 7 6.77 5.08 5.90 6.90 9.30 6.79 4.22

  18. R Chart Control Limits Solution

  19. R Chart Control Chart Solution UCL R-bar LCL

  20. X Chart • Type of variables control chart • Shows sample means over time • Monitors process average • Example: Weigh samples of coffee & compute means of samples; Plot

  21. From Table Mean of sample i Range of sample i # Samples X Chart Control Limits

  22. X Chart Hotel Data Sample DayDelivery TimeMean Range 1 7.30 4.20 6.10 3.45 5.55 5.32 3.85 2 4.60 8.70 7.60 4.43 7.62 6.59 4.27 3 5.98 2.92 6.20 4.20 5.10 4.88 3.28 4 7.20 5.10 5.19 6.80 4.21 5.70 2.99 5 4.00 4.50 5.50 1.89 4.46 4.07 3.61 6 10.10 8.10 6.50 5.06 6.94 7.34 5.04 7 6.77 5.08 5.90 6.90 9.30 6.79 4.22

  23. X Chart Control Limits Solution*

  24. X ChartControl Chart Solution* UCL X-bar LCL

  25. X AND R CHART EXAMPLEIN-CLASS EXERCISE The following collection of data represents samples of the amount of force applied in a gluing process: Determine if the process is in control by calculating the appropriate upper and lower control limits of the X-bar and R charts.

  26. X AND R CHART EXAMPLEIN-CLASS EXERCISE

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

  28. Example of x-bar and R charts: Step 2. Determine Control Limit Formulas and Necessary Tabled Values

  29. Example of x-bar and R charts: Steps 3&4: Calculate R-chart and Plot Values

  30. Example of x-bar and R charts: Steps 5&6. Calculate x-bar Chart and Plot Values

  31. SOLUTION:Example of x-bar and R charts: 1. Is the process in Control? 2. If not, what could be the cause for the process being out of control?

  32. Process Capability • Process limits - • Tolerance limits - -

  33. 1. Make bigger 2. Make smaller Process Capability • How do the limits relate to one another? You want: tolerance range > process range Two methods of accomplishing this:

  34. Process Capability Measurement Cp index = Tolerance range / Process range What value(s) would you like for Cp?

  35. LTL UTL 6s 6s

  36. LTL UTL 12s 6s

  37. 6s • While the Cp index provides useful information on process variability, it does not give information on the process average relative to the tolerance limits. Note: LTL UTL 12s

  38. = estimate of theprocess mean s= estimate of thestandard deviation Cpk Index This process capability index shows how well parts being produced conform to design specifications.

  39. LTL UTL 3s 9s 3s 3s

  40. Example use of process capability indices The design specifications for a machined slot is 0.5± .003 inches. Samples have been taken and the process mean is estimated to be 0.501. The process standard deviation is estimated to be 0.001. What can you say about the capability of this process to produce this dimension?

  41. Process capability The CP K ratio gives “true” information about process capability Machined slot (inches) 0.497 inches LTL 0.503 inches UTL  = 0.001 inches Process mean 0.501 inches

  42. Basic Forms of Statistical Sampling for Quality Control • Sampling to accept or reject the immediate lot of product at hand • Sampling to determine if the process is within acceptable limits

  43. Acceptance Sampling • Purposes • Advantages

  44. Acceptance Sampling • Disadvantages

  45. Risk • Acceptable Quality Level (AQL) • Maximum level of defects for the lot to be considered “high quality” • a (Producer’s risk) • The probability of rejecting a “high quality” lot • Lot Tolerance Percent Defective (LTPD) • Level of defects allowed before the lot is considered “low quality” •  (Consumer’s risk) • The probability of accepting a “low quality” lot

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