00350 Çb53a2c6306feffa8a42cd1d2e437fc

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Prairie & Zimmer

From (8], the sample size necessary to obtain a lower one-sided 100 (l-y)% confidence limit Ql oⁿ the parameter Q can be computed for an observed number of failures x.

If a 50% lower confidence limit Ql is desired, 1 - y = .50, Zi_y = 0 and the necessary sample size n is

[9]

where A = 1/Ql and B = 1/3Ql •

Thus for a 50% lower confidence limit Ql, the relationship between the necessary sample size and the observed number of failures is an approximate simple linear relationship. For example, at Ql = .05 and x = 3, n » 2.673/.05 w 54. Thus, if the third failure occurs on or after the 54^ test unit and the reliability requirement is .95, sampling would continue on a probational basis.

Plan Characterization

The plans are characterized in three ways: the first is by the number of units that will be tested during production given no test units fail; the second is by the expected number of defective units accepted after on unanticipated decrease in product reliability for different sampling rates and test times; and the third by the usual, operating characteristic (OC) concepts such as percent inspected versus fraction defective and outgoing fraction defective versus fraction defective. Since the primary purpose of these plans is to monitor quality and reliability it is unlikely that the true failure probability would stay constant in the event of failure. In practice, if a significant problem were discovered it would be fixed before production would be continued. As a result, the usual OC characteristics do not carry the same importance as they do in conventional lot or continuous sampling. The OC curves are most easily obtained by Computer simulation.

The number of units tested if no failures occur in a total production of N units is