An Exact Distribution - Free Analysis for Accelerated Life Testing at Several Levels of a Single Stress

Abstract

Consider the following experiment: At stress levels x₁ < … < x_k, n₁, …, 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) = Φ[g(t, x)], where g is a real-valued function specified up to an unknown parameter c, and Φ 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 _o, x_o) for specified t _o and x_o. 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.

KEY WORDS:

• Kolomogorov–Smirnov test
• Power rule
• Nonparametrics
• Arrhenius model
• cyring model