00346 Ï1855119a345b49152255d7988b4dca

350

Prairie & Zimmer

Table 1. c Yalue

.95	.96	.97	.98	.99	.995	.999	R
7	9	12	18	36	71	357	P=.70
4	5	7	10	20	40	223	P=.80
2	3	4	5	10	21	105	P=.90
1	1	2	3	5	10	51	P=.95

no failures during the initial sampling if the true failure ratÄ™ coincides with the reÄ…uirement and the value c is used. For the binomial assumption, P = R^e and for the Poisson approximation to the binomial, P = ^{e c}° or -ln P = c(l-R).

In FigurÄ™ 2, Pk values are presented on semi-log paper where Pk is the chance of getting c consecutive successes when the true failure ratÄ™ is K(1 -R) and R is the reliability reÄ…uirement. When K = 1, notÄ™ that the true failure ratÄ™ is 1 - R, Pk = 1 ⁼ c(l - R) and the P values given in FigurÄ™ 2 are the values given in Table 1 for the appropriate c's and R's. With the Poisson approximation to the binomial, -ln Pk = cK(l - R). That is, ln Pk and K have a linear relationship as presented in FigurÄ™ 2. For example, when the reliability reÄ…uirement is 0.99 and c = 20 is selected, the chance of getting 20 consecutive successes when the true failure ratÄ™ is 0.01 is approximately 0.80 which is given in Table 1 and in FigurÄ™ 2 with K = 1. When the true failure ratÄ™ is 10 times that, K = 10, the chance of getting 20 consecutive successes is 0.10. At the .999 reliability reÄ…uirement, a lower value of c than the value given in Table 1 is recommended as a practical upper limit.

Level 1 Sampling After successful completion of the initial testing, the sampling ratÄ™ can be reduced to 100 P\%. Sampling continues at 100 Pi% until c consecutive sampled units have been tested with no failures. If there are no failures, the sampling ratÄ™ can be fiuther reduced to 100 P2%.

Level 2 Sampling After successful completion of Level 1 sampling, the sampling ratÄ™ can be reduced to 100 P2% until a failure occurs. A failure causes the sampling ratÄ™ to revert to initial sampling, unless the assessed failure ratÄ™ is concordant with the reÄ…uirement and the failure modÄ™ is not new and