CHAPTER 27 • Statistical Process Control

27-46 CHAPTER 27 • Statistical Process Control
(c) Explain why a p chart is of no use at such high levels of
quality.
27.54 Manufacturing isn’t everything. Because the manufacturing
quality in the previous exercise is so high, the
process of writing up orders is the major source of quality
problems: the defect rate there is 9000 per million opportunities.
The manufacturer processes about 600 orders per
month.
(a) What is p for the order-writing process? How many defective
orders do you expect to see in a month?
(b) What are the center line and control limits for a p chart
for plotting monthly proportions of defective orders? What is
the smallest number of bad orders in a month that will result
in a point above the upper control limit?
Table 27.9 gives process control samples for a study of response
times to customer calls arriving at a corporate call center. A sample
of 6 calls is recorded each shift for quality improvement purposes.
The time from the first ring until a representative answers the call
is recorded. Table 27.9 gives data for 50 shifts, 300 calls total. 16
Exercises 27.55 to 27.57 make use of this setting.
TABLE 27.9 Fifty control chart samples of call center response times
(seconds)
SAMPLE STANDARD
SAMPLE TIME MEAN DEVIATION
1 59 13 2 24 11 18 21.2 19.93
2 38 12 46 17 77 12 33.7 25.56
3 46 44 4 74 41 22 38.5 23.73
4 25 7 10 46 78 14 30.0 27.46
5 6 9 122 8 16 15 29.3 45.57
6 17 17 9 15 24 70 25.3 22.40
7 9 9 10 32 9 68 22.8 23.93
8 8 10 41 13 17 50 23.2 17.79
9 12 82 97 33 76 56 59.3 32.11
10 42 19 14 21 12 44 25.3 14.08
11 63 5 21 11 47 8 25.8 23.77
12 12 4 111 37 12 24 33.3 39.76
13 43 37 27 65 32 3 34.5 20.32
14 9 26 5 10 30 27 17.8 10.98
15 21 14 19 44 49 10 26.2 16.29
16 24 11 10 22 43 70 30.0 22.93
17 27 10 32 96 11 29 34.2 31.71
18 7 28 22 17 9 24 17.8 8.42
19 15 14 34 5 38 29 22.5 13.03
20 16 65 6 5 58 17 27.8 26.63
21 7 44 14 16 4 46 21.8 18.49
22 32 52 75 11 11 17 33.0 25.88
23 31 8 36 25 14 85 33.2 27.45
24 4 46 23 58 5 54 31.7 24.29
25 28 6 46 4 28 11 20.5 16.34
26 111 6 3 83 27 6 39.3 46.34
27 83 27 2 56 26 21 35.8 28.88
28 276 14 30 8 7 12 57.8 107.20
29 4 29 21 23 4 14 15.8 10.34
30 23 22 19 66 51 60 40.2 21.22
31 14 111 20 7 7 87 41.0 45.82
32 22 11 53 20 14 41 26.8 16.56