Hardness Assurance and Overtesting

A procedure is developed for estimating the advantage gained by testing electronic piece parts at levels of radiation higher than the specification level which they must survive. When the probability distribution of radiation stress to failure is approximately lognormal, and a test shows that with confidence, C, the survival probability is at least PT at the test level of stress RT, then with the same confidence the survival probability is at least PS at a lower specification level of stress RS where, Ps = F[ F¿(PT) + ln(RT/RS/¿ln(MAX)] The standard deviation, ¿ln(MAX), is the estimated maximum s.d. in the logarithms of stress to failure; the function, F(X), is the standard normal cumulative probability distribution function; and the function, F(P), is the antifunction of F(X) - that is, F(P) standard deviations above the mean of a normal distribution includes fraction P of the distribution. A discussion is given of how this formula also applies to those tests which are more properly acceptance/rejection tests rather than tests which establish a confidence that parts will survive a given radiation level with a given probability. The suggested overtesting technique is compared to other standard testing techniques.