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An exact distribution-free analysis for accelerated life testing at several levels of a single stress. (English) Zbl 0588.62177

Consider the following experiment: At stress levels \(x_ 1<...<x_ k,\quad n_ 1,...,n_ k\) items are put on test. The failure times of those items failing before times \(t^*\!_ 1,...,t^*\!_ k\) are recorded, and the remaining failure times are censored. Let P(t,x) denote the probability that an item stressed at level x fails on or before time t. We consider models of the form \(P(t,x)=\Phi [g(t,x)]\), where g is a real-valued function specified up to an unknown parameter c, and \(\Phi\) is an unspecified continuous distribution function.
Under these assumptions a Kolmogorov-Smirnov-type test is discussed as a method for estimating c as well as \(P(t_ 0,x_ 0)\) for specified \(t_ 0\) and \(x_ 0\). The method is exact and does not require failures at unaccelerated stress levels. If \(n_ 1=...=n_ k\), the method extends to experiments that at each stress level are terminated after a specified number of failures is observed.

MSC:

62N05 Reliability and life testing
62G10 Nonparametric hypothesis testing
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