a. Explanation Calculation: The given information is that C chart is an alternative to U chart the number of defects chart. The 3 sigma control limits are given below: U C L = n u ¯ + 3 n u ¯ L C L = n u ¯ − 3 n u ¯ Verification: Consider a random variable X which represents the number of defects in a sample of size n . Then the random variable X is assumed to follow Poisson distribution since, The number of defects represents the random occurrence of an event . The occurrence of defects is independent of each other. By Poisson distribution, the expected value is, E ( X ) = λ Where, λ represents the mean occurrence of the event. Here, Instead of λ the average number of defects u ¯ is substituted by multiplying with n b. To determine Apply C chart to the data given in Example 15-5. c. To determine Identify whether the C chart gives an equivalent result as U chart.

Applied Statistics and Probability for Engineers

6th Edition

ISBN: 9781118539712

Author: Douglas C. Montgomery

Publisher: WILEY

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Question

Chapter 15, Problem 139SE

To determine

Verify that the given control limits are correct.

To determine

Apply C chart to the data given in Example 15-5.

To determine

Identify whether the C chart gives an equivalent result as U chart.

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Chapter 15, Problem 138SE

Chapter 15, Problem 140SE

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Chapter 15 Solutions

Applied Statistics and Probability for Engineers

Ch. 15.3 - 15-1. Control charts for and R are to be set up...Ch. 15.3 - 15-2. Twenty-five samples of size 5 are drawn from...Ch. 15.3 - 15-3. Control charts are to be constructed for...Ch. 15.3 - 15-4. Samples of size n = 6 are collected from a...Ch. 15.3 - 15-5. The level of cholesterol (in mg/dL) is an...Ch. 15.3 - 15-6. An control chart with three-sigma control...Ch. 15.3 - 15-7. An extrusion die is used to produce aluminum...Ch. 15.3 - 15-8. The copper content of a plating bath is...Ch. 15.3 - 15-9. The pull strength of a wire-bonded lead for...Ch. 15.3 - 15-10. The following data were considered in...

Ch. 15.3 - 15-11. The thickness of a metal part is an...Ch. 15.3 - 15-12. Apply the Western Electric Rules to the...Ch. 15.3 - 15-13. Apply the Western Electric Rules to the...Ch. 15.3 - 15-14. Web traffic can be measured to help...Ch. 15.3 - 15-15. Consider the data in Exercise 15-9....Ch. 15.3 - 15-16. Consider the data in Exercise 15-10....Ch. 15.3 - 15-17. An X control chart with 3-sigma control...Ch. 15.3 - 15-18. An article in Quality & Safety in Health...Ch. 15.4 - 15-19. Twenty successive hardness measurements are...Ch. 15.4 - 15-20. In a semiconductor manufacturing process,...Ch. 15.4 - 15-21. O An automatic sensor measures the diameter...Ch. 15.4 - 15-22. The viscosity of a chemical intermediate is...Ch. 15.4 - 15-23. The following table of data was analyzed in...Ch. 15.4 - 15-24. Pulsed laser deposition technique is a thin...Ch. 15.4 - 15-25. The production manager of a soap...Ch. 15.4 - 15-26. An article in Quality & Safety in Health...Ch. 15.4 - 15-27. An article in Journal of the Operational...Ch. 15.5 - 15-28. Suppose that a quality characteristic is...Ch. 15.5 - 15-29. Suppose that a quality characteristic is...Ch. 15.5 - 15-30. Suppose that a quality characteristic is...Ch. 15.5 - 15-31. A normally distributed process uses 66.7%...Ch. 15.5 - 15-32. A normally distributed process uses 85% of...Ch. 15.5 - 15-33. Reconsider Exercise 15-1. Suppose that the...Ch. 15.5 - 15-34. Reconsider Exercise 15-2 in which the...Ch. 15.5 - 15-35. Reconsider Exercise 15-3. Suppose that the...Ch. 15.5 - 15-36. Reconsider Exercise 15-4(a). Assuming that...Ch. 15.5 - 15-37. Reconsider the diameter measurements in...Ch. 15.5 - 15-38. Reconsider the copper-content measurements...Ch. 15.5 - 15-39. Reconsider the pull-strength measurements...Ch. 15.5 - 15-40. Reconsider the syringe lengths in Exercise...Ch. 15.5 - 15-41. Reconsider the hardness measurements in...Ch. 15.5 - 15-42. Reconsider the viscosity measurements in...Ch. 15.5 - 15-43. Suppose that a quality characteristic is...Ch. 15.5 - 15-44. Suppose that a quality characteristic is...Ch. 15.5 - 15-45. An control chart with 3-sigma control...Ch. 15.5 - 15-46. A control chart for individual observations...Ch. 15.5 - 15-47. A process mean is centered between the...Ch. 15.5 - 15-48. The PCR for a measurement is 1.5 and the...Ch. 15.6 - 15-49. An early example of SPC was described in...Ch. 15.6 - 15-50. Suppose that the following fraction...Ch. 15.6 - 15-51. The following are the numbers of defective...Ch. 15.6 - 15-52. The following represent the number of...Ch. 15.6 - 15-53. The following represent the number of...Ch. 15.6 - 15-54. Consider the data on the number of...Ch. 15.6 - 15-55. In a semiconductor manufacturing company,...Ch. 15.6 - Prob. 56E Ch. 15.6 - Prob. 57E Ch. 15.6 - Prob. 58E Ch. 15.7 - Prob. 59E Ch. 15.7 - Prob. 60E Ch. 15.7 - 15-61. Consider the control chart in Fig. 15-3....Ch. 15.7 - Prob. 62E Ch. 15.7 - Prob. 63E Ch. 15.7 - Prob. 64E Ch. 15.7 - Prob. 65E Ch. 15.7 - Prob. 66E Ch. 15.7 - Prob. 67E Ch. 15.7 - Prob. 68E Ch. 15.7 - Prob. 69E Ch. 15.7 - 15-70. Consider an control chart with UCL =...Ch. 15.7 - Prob. 71E Ch. 15.7 - Prob. 72E Ch. 15.8 - Prob. 73E Ch. 15.8 - Prob. 74E Ch. 15.8 - Prob. 75E Ch. 15.8 - Prob. 76E Ch. 15.8 - Prob. 77E Ch. 15.8 - Prob. 78E Ch. 15.8 - Prob. 79E Ch. 15.8 - Prob. 80E Ch. 15.8 - Prob. 81E Ch. 15.8 - 15-82. A process has a target of μ0 = 100 and a...Ch. 15.8 - 15-83. Heart rate (in counts/minute) is measured...Ch. 15.8 - Prob. 84E Ch. 15.8 - Prob. 85E Ch. 15.8 - Prob. 86E Ch. 15.9 - Prob. 87E Ch. 15.9 - Prob. 88E Ch. 15.9 - Prob. 89E Ch. 15.9 - Prob. 90E Ch. 15 - Prob. 91SE Ch. 15 - 15-92. Rework Exercise 15-91 with and S...Ch. 15 - Prob. 93SE Ch. 15 - Prob. 94SE Ch. 15 - 15-95. An article in Quality Engineering [“Is the...Ch. 15 - Prob. 96SE Ch. 15 - Prob. 97SE Ch. 15 - Prob. 98SE Ch. 15 - Prob. 99SE Ch. 15 - Prob. 100SE Ch. 15 - Prob. 101SE Ch. 15 - Prob. 102SE Ch. 15 - Prob. 103SE Ch. 15 - Prob. 104SE Ch. 15 - Prob. 105SE Ch. 15 - Prob. 106SE Ch. 15 - Prob. 107SE Ch. 15 - Prob. 108SE Ch. 15 - 15-109. The depth of a keyway is an important part...Ch. 15 - Prob. 110SE Ch. 15 - Prob. 111SE Ch. 15 - Prob. 112SE Ch. 15 - Prob. 113SE Ch. 15 - Prob. 114SE Ch. 15 - Prob. 115SE Ch. 15 - Prob. 117SE Ch. 15 - Prob. 118SE Ch. 15 - 15-119. Consider an control chart with UCL =...Ch. 15 - Prob. 120SE Ch. 15 - Prob. 121SE Ch. 15 - Prob. 122SE Ch. 15 - Prob. 123SE Ch. 15 - Prob. 124SE Ch. 15 - Prob. 125SE Ch. 15 - Prob. 126SE Ch. 15 - Prob. 127SE Ch. 15 - Prob. 128SE Ch. 15 - Prob. 129SE Ch. 15 - Prob. 130SE Ch. 15 - Prob. 131SE Ch. 15 - 15-132. Consider an control chart with k-sigma...Ch. 15 - Prob. 133SE Ch. 15 - Prob. 134SE Ch. 15 - Prob. 135SE Ch. 15 - Prob. 136SE Ch. 15 - 15-137. Consider a process whose specifications on...Ch. 15 - Prob. 138SE Ch. 15 - Prob. 139SE Ch. 15 - Prob. 140SE Ch. 15 - Prob. 141SE

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