The Robustness of Life Testing Procedures Derived from the Exponential Distribution

Almost all the statistical procedures in current use for evaluating the reliability of components or equipment rest on the assumption that the failure times follow the exponential distribution. However, in practical situations one rarely has enough data to determine whether failure times are actually exponential. This paper studies the behavior of several statistical life testing procedures based on the exponential failure law if the true failure law is the Weibull distribution. It is found that these statistical techniques, which are widely used, are very sensitive to departures from initial assumptions. Applying these techniques to lie test data when the exponential failure law is not satisfied may result in substantially increasing the probability of accepting components or equipments having poor mean-timsto-failure. This paper also develops convenient analytic techniques for approximating (i) the distribution of sums of independent random variables, and (ii) the characteristics of sequential procedures, for non-negative random variables. These techniques are based on a general life distribution which consists of an expansion of generalized Laguerre polynomials. Application of these methods to the Weibull distribution yields excellent results.