Solutions to Chapter 3 Exercises

Solutions to Chapter 3 Exercises Chapter 3: Quality Management

Exercise 1 Chapter 3: Quality Management

Exercise 2 continued The upward trend in cancellations and non-renewals is a definite cause for concern. Chapter 3: Quality Management

Exercise 3 concluded 1.2826 1.02 .7574 UCL * * * * * * LCL Jun Jul Aug Sep Oct Nov Chapter 3: Quality Management

Exercise 4 Xi 3,500 4,100 3,750 4,300 4,000 3,650 Total 23,300 Chapter 3: Quality Management

Exercise 5 concluded Normally control limits are set at three sigma so any point outside the limits is to be investigated. For limits set at lower sigma values, it should be considered that there is a chance of a random point falling outside the limits even though the process is in control. For one-sigma limits the chance is 32% or one out of three points. For two-sigma limits the chance is 5%, or one point out of twenty. In our case there are 3 points out of twelve, so action should be taken, but if these had been one-sigma limits, action would be unnecessary. Chapter 3: Quality Management

Exercise 6a DayRange Sat 3 Sun 4 Mon 2 Tue 5 Wed 3 Thu 5 Sum 22 For Friday the range is 7, so the range on Friday is in control. Chapter 3: Quality Management

Exercise 6a concluded 9.45 3.67 0 UCL * * * * * * * LCL Sat Sun Mon Tue Wed Thu Fri Chapter 3: Quality Management

Exercise 6b DaySample Mean Sat 20.3 Sun 19.3 Mon 17.0 Tue 19.0 Wed 21.0 Thu 18.7 Sum 115.3 For Friday the sample mean is 16.7, so the process is in control. Chapter 3: Quality Management

Exercise 6b concluded 22.96 19.21 15.45 UCL * * * * * * * LCL Sat Sun Mon Tue Wed Thu Fri Chapter 3: Quality Management

Exercise 7 Dough Boy’s pizza crust production system is not capable of consistently meeting its customer requirements given the Cpindex of less than 1. Options available to Dough Boy include improving its production system to lower the natural variation in the system. In this case, Dough Boy needs to reduce the standard deviation of pizza crusts from 1.1 to .66 or lower in order to obtain a Cpindex of 1 or more. Alternatively, Dough Boy could try to convince its customers to increase the range of acceptable pizza crust diameters.

Exercise 8 The Cp index indicates that given the natural variation in the filling operation, it is capable of meeting the design specifications. However, when the alignment of the process mean and the design specification is considered, it is found that the filling operation is not capable of consistently meeting design requirements. Chapter 3: Quality Management

Exercise 9a Total number of cases = 27,400 Total incorrect = 235 Chapter 3: Quality Management

Exercise 9a concluded .03623 .00857 0.0 UCL LCL Chapter 3: Quality Management

Exercise 9b: Day 7 On day 7, p = .0115, therefore process is in control. Chapter 3: Quality Management

Exercise 10 Xp c Mon 25 .000025 25 Tue 36 .000036 36 Wed 17.00001717 Sum 78 .000078 78 Avg. 26 .000026 26 Chapter 3: Quality Management

Exercise 10: Sample Means Chart A2 = 1.023; Range 36 - 17 = 19 UCL = 26 + 1.023(19) = 45.44 LCL = 26 - 1.023(19) = 6.56 Thursday’s 47 defectives is outside control limits. Chapter 3: Quality Management

Exercise 10: p chart On Thursday, p = .000047, therefore not in control. Chapter 3: Quality Management

Exercise 10: c chart On Thursday, 47 are defective. Thus, out of control. Chapter 3: Quality Management

Exercise 10 concluded • The c chart is most appropriate • The p chart is acceptable • The sample means chart is not appropriate Chapter 3: Quality Management

Solutions to Chapter 3 Exercises