This example illustrates the analysis of binomial proportions of capacitor failures from nine circuit boards. The data are given by Nelson (1982, p. 451) . The following statements create and list a SAS data set named BINEX containing the data:

data binex;
   input board sample fail;
   datalines;
1 84 2
2 72 3
3 72 5
4 119 19
5 538 21
6 51 2
7 517 9
8 462 18
9 143 2
;

Figure 14.41 displays a listing of the data. The variable Board identifies the circuit board, the variable Sample provides the number of capacitors on the boards, and the variable Fail provides the number of capacitors failing on the boards.

The following statements analyze the proportion of capacitors failing:

proc reliability data=Binex;
   distribution binomial;
   analyze fail(sample) = board / predict(1000)
                                  tolerance(.05);
run;

The DISTRIBUTION statement specifies the binomial distribution. The analysis requested with the ANALYZE statement consists of tabular output only. Graphical output is not available for the binomial distribution. The variable Fail provides the number of capacitors failing on each board, the variable Sample provides the sample size (number of capacitors) for each board, and the variable Board identifies the individual boards. The statement option PREDICT(1000) requests the predicted number of capacitors failing and prediction limits in a future sample of size 1000. The option TOLERANCE(.05) requests the sample size required to estimate the binomial proportion to within 0.05. Figure 14.42 displays the results of the analysis.

The "Pooled Data Analysis" table displays the estimated binomial probability and exact binomial confidence limits when data from all boards are pooled. The chi-square value and p-value for a test of equality of the binomial probabilities for all of the boards are also shown. In this case, the p-value is less than 0.05, so you reject the test of equality at the 0.05 level.

The "Predicted Values and Limits" table provides the predicted failure count and prediction limits for the number of capacitors that would fail in a future sample of size 1000 for the pooled data, as requested with the PREDICT(1000) option. The "Sample Size for Estimation" table gives the sample size required to estimate the binomial probability to within 0.05 for the pooled data, as requested with the TOLERANCE(.05) option.

The "Estimates by Group" table supplies the estimated binomial probability, confidence limits, and the contribution to the total chi-square for each board. The pooled values are shown in the last line of the table.

The "Predicted Values by Group" table gives the predicted counts in a future sample of size 1000, prediction limits, and the sample size required to estimate the binomial probability to within the tolerance of 0.05 for each board. Values for the pooled data are shown in the last line of the table.