Applied Statistics and Probability for Engineers
6th Edition
ISBN: 9781118539712
Author: Douglas C. Montgomery
Publisher: WILEY
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Chapter 15, Problem 115SE
a.
To determine
Find the ARL for the process having no shift in the
Find the ARL value for the process to detect the shift when the process mean is 12.
b.
To determine
Find the ARL for the process having no shift in the mean.
Find the ARL value for the process to detect the shift when the process mean is 12.
Give conclusions.
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Questions
An insurance company's cumulative incurred claims for the last 5 accident years are given
in the following table:
Development Year
Accident Year 0
2018
1 2 3 4
245 267 274 289 292
2019
255 276 288 294
2020
265 283 292
2021
263 278
2022
271
It can be assumed that claims are fully run off after 4 years. The premiums received for
each year are:
Accident Year Premium
2018
306
2019
312
2020
318
2021
326
2022
330
You do not need to make any allowance for inflation.
1. (a) Calculate the reserve at the end of 2022 using the basic chain ladder method.
(b) Calculate the reserve at the end of 2022 using the Bornhuetter-Ferguson method.
2. Comment on the differences in the reserves produced by the methods in Part 1.
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. 56ECh. 15.6 - Prob. 57ECh. 15.6 - Prob. 58ECh. 15.7 - Prob. 59ECh. 15.7 - Prob. 60ECh. 15.7 - 15-61. Consider the control chart in Fig. 15-3....Ch. 15.7 - Prob. 62ECh. 15.7 - Prob. 63ECh. 15.7 - Prob. 64ECh. 15.7 - Prob. 65ECh. 15.7 - Prob. 66ECh. 15.7 - Prob. 67ECh. 15.7 - Prob. 68ECh. 15.7 - Prob. 69ECh. 15.7 - 15-70. Consider an control chart with UCL =...Ch. 15.7 - Prob. 71ECh. 15.7 - Prob. 72ECh. 15.8 - Prob. 73ECh. 15.8 - Prob. 74ECh. 15.8 - Prob. 75ECh. 15.8 - Prob. 76ECh. 15.8 - Prob. 77ECh. 15.8 - Prob. 78ECh. 15.8 - Prob. 79ECh. 15.8 - Prob. 80ECh. 15.8 - Prob. 81ECh. 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. 84ECh. 15.8 - Prob. 85ECh. 15.8 - Prob. 86ECh. 15.9 - Prob. 87ECh. 15.9 - Prob. 88ECh. 15.9 - Prob. 89ECh. 15.9 - Prob. 90ECh. 15 - Prob. 91SECh. 15 - 15-92. Rework Exercise 15-91 with and S...Ch. 15 - Prob. 93SECh. 15 - Prob. 94SECh. 15 - 15-95. An article in Quality Engineering [“Is the...Ch. 15 - Prob. 96SECh. 15 - Prob. 97SECh. 15 - Prob. 98SECh. 15 - Prob. 99SECh. 15 - Prob. 100SECh. 15 - Prob. 101SECh. 15 - Prob. 102SECh. 15 - Prob. 103SECh. 15 - Prob. 104SECh. 15 - Prob. 105SECh. 15 - Prob. 106SECh. 15 - Prob. 107SECh. 15 - Prob. 108SECh. 15 - 15-109. The depth of a keyway is an important part...Ch. 15 - Prob. 110SECh. 15 - Prob. 111SECh. 15 - Prob. 112SECh. 15 - Prob. 113SECh. 15 - Prob. 114SECh. 15 - Prob. 115SECh. 15 - Prob. 117SECh. 15 - Prob. 118SECh. 15 - 15-119. Consider an control chart with UCL =...Ch. 15 - Prob. 120SECh. 15 - Prob. 121SECh. 15 - Prob. 122SECh. 15 - Prob. 123SECh. 15 - Prob. 124SECh. 15 - Prob. 125SECh. 15 - Prob. 126SECh. 15 - Prob. 127SECh. 15 - Prob. 128SECh. 15 - Prob. 129SECh. 15 - Prob. 130SECh. 15 - Prob. 131SECh. 15 - 15-132. Consider an control chart with k-sigma...Ch. 15 - Prob. 133SECh. 15 - Prob. 134SECh. 15 - Prob. 135SECh. 15 - Prob. 136SECh. 15 - 15-137. Consider a process whose specifications on...Ch. 15 - Prob. 138SECh. 15 - Prob. 139SECh. 15 - Prob. 140SECh. 15 - Prob. 141SE
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