A non-parametric estimation procedure for accelerated life tests with two stresses
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Accelerated life testing is concerned with subjecting long life items to a series of stress levels higher than those experienced under normal conditions so as to obtain the lifetime distribution of the items under normal stress levels. A parametric approach to this problem requires two assumptions. Firstly, the lifetime of the item is assumed to have the same distribution under all stress levels. In other words, we assume that a change of stress does not change the shape of the life distribution but changes only its scale. Secondly, a functional relationship referred to as the time transformation function is assumed between the parameters of the life distribution and the accelerating stress(es). On the other hand, a non-parametric approach may not require either one of these assumptions. We drop the first of the two assumptions and treat the problem partially non-parametrically. We develop a non-parametric estimation procedure for two versions of the generalized Arrhenius model with two stress variables assuming a linear acceleration function. We use it to obtain consistent estimates of the parameters of the life distribution under normal stress levels and compare our non-parametric method with parametric methods assuming exponential, Weibull and lognormal life distributions using some real life and simulated data.