Question

The x-bar and R values for 20 samples of size five are shown in Table 10E.6. Specifications on this product have been established as 0.550   +/- 0.02.

Table 10.E.8

Sample No.	X Bar	R
1	0.549	0.0025
2	0.548	0.0021
3	0.548	0.0023
4	0.551	0.0029
5	0.553	0.0018
6	0.552	0.0017
7	0.550	0.0020
8	0.551	0.0024
9	0.553	0.0022
10	0.556	0.0028
11	0.547	0.0020
12	0.545	0.0030
13	0.549	0.0031
14	0.552	0.0022
15	0.550	0.0023
16	0.548	0.0021
17	0.556	0.0019
18	0.546	0.0018
19	0.550	0.0021
20	0.551	0.022

(a) Construct a modified control chart with α=0.0013, assuming that if the true process

fraction nonconforming is as large as 1%, the process is unacceptable.

(b) Suppose that if the true process fraction nonconforming is as large as 1%, we would like an

acceptance control chart to detect this out-of control condition with probability 0.90.

Construct this acceptance control chart, and compare it to the chart obtained in part (a).

Answer 1