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Answers to Selected Exercises
Chapter 2

Chapter 3

1 . S ^{2} = 7.3. Adding a constant to every number in a sample does not change the value of S ^{2} .
5 . (a) 0.95053; (d) 0.9545; (e) z _{0} = 1.96.
7 . .
9 . 0.06681. The probability is approximate since the particular probability distribution was not stated.
15 . 2. We have 3% as the estimate of the proportion nonconforming, and conclude that the process needs improving.
17 . 0.9727.
22 . (c)
Chapter 4

5 . The control limits could be adjusted or a control chart of residuals could be used.
20 . 80.5
Chapter 5

2 . 13, 2.
3 . The moving ranges and moving averages are correlated so interpreting the charts can be difficult.
5 . An chart is more sensitive in detecting a shift in the process mean (as the answers to exercise 2 indicate).
Chapter 6

1 . 0.0462 and 0.2583.
3 . Because there will not be a lower control limit.
Chapter 7

3 . (a) ; (c) decrease, 0.02278 (before), 0.0027 (after).
5 . 1.479, no.
Chapter 8

2 . (a) 5.75 assuming a basic CUSUM scheme; (b) 15.
3 . When doubt exists as to whether or not an assignable cause was removed.
Chapter 9

Chapter 11

2 . (a) No outliers are identified; (b) the estimate of sigma is 3.21.
Chapter ...

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