A nonparametric approach to accelerated life testing under multiple stresses

Accelerated life testing (ALT) is concerned with subjecting items to a series of stresses at several levels higher than those experienced under normal conditions so as to obtain the lifetime distribution of items under normal levels. A parametric approach to this problem requires two assumptions. First, the lifetime of an item is assumed to have the same distribution under all stress levels, that is, a change of stress level does not change the shape of the life distribution but changes only its scale. Second, a functional relationship is assumed between the parameters of the life distribution and the accelerating stresses. A nonparametric approach, on the other hand, assumes a functional relationship between the life distribution functions at the accelerated and nonaccelerated stress levels without making any assumptions on the forms of the distribution functions. In this paper, we treat the problem nonparametrically. In particular, we extend the methods of Shaked, Zimmer, and Ball [7] and Strelec and Viertl [8] and develop a nonparametric estimation procedure for a version of the generalized Arrhenius model with two stress variables assuming a linear acceleration function. We obtain consistent estimates as well as confidence intervals of the parameters of the life distribution under normal stress level and compare our nonparametric method with parametric methods assuming exponential, Weibull and lognormal life distributions using both real life and simulated data.