A likelihood ratio test for a shift in the lifelength distribution

Abstract

In this article, we discuss the problem of detecting the effect of a shock occurring in a life test experiment involving n test specimens. It is assumed that a shock occurs at the (n - r)th failure where r is known. Such a shock is suspected to have altered the parameters of the remaining lifelengths of the surviving specimens. Under this set-up, a test based on likelihood ratio criterion is discussed. It has been shown that when the lifelength distribution is exponential, the null distribution of the proposed test statistic is beta of type I with parameters r and (n - r). The distribution of the proposed test statistic under alternate hypothesis and the exact form of the power function have been derived. A power comparison of the proposed test statistic is also made with a prediction-based test statistic discussed in the literature. Copyright © 1998 by Marcel Dekker, Inc.