Question 10.9: In the production of silicon wafers, 30 lots of size 500 are......

ISE Principles of Statistics for Engineers and Scientists [987713]

In the production of silicon wafers, 30 lots of size 500 are sampled, and the proportion of defective wafers is calculated for each sample. Table 10.2 presents the results. Compute the center line and 3𝜎 control limits for the p chart. Plot the chart. Does the process appear to be in control?

TABLE 10.2 Number and proportion defective, for Example 10.9
Sample	Number Defective	Proportion Defective (p̂)	Sample	Number Defective	Proportion Defective (p̂)
1	17	0.034	16	26	0.052
2	26	0.052	17	19	0.038
3	31	0.062	18	31	0.062
4	25	0.050	19	27	0.054
5	26	0.052	20	24	0.048
6	29	0.058	21	22	0.044
7	36	0.072	22	24	0.048
8	26	0.052	23	30	0.060
9	25	0.050	24	25	0.050
10	21	0.042	25	26	0.052
11	18	0.036	26	28	0.056
12	33	0.066	27	22	0.044
13	29	0.058	28	31	0.062
14	17	0.034	29	18	0.036
15	28	0.056	30	23	0.046

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The average of the 30 sample proportions is $\overline{p} = 0.050867$ . The center line is therefore plotted at 0.050867. The control limits are plotted at $0.050867± 3 \sqrt{(0.050867)(0.949133) ∕ 500}$ . The upper control limit is therefore 0.0803, and the lower control limit is 0.0214. Figure 10.14 presents the p chart. The process appears to be in control.

10.14

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