Accelerated Life Testing

Abstract

In industry the failure time data are used for product reliability estimation. Failures of highly reliable units are rare and other information should be used than traditional censored failure time data. One way of obtaining this complementary reliability information is to apply the methods of the so-called accelerated life-testing (ALT). The purpose of the ALT is to give estimators of the main reliability characteristics under usual (design) stress using data of accelerated experiments when units are tested at higher than usual stress conditions, i.e. in ALT is supposed to use higher levels of experimental time varying factors or covariates (such as temperature, voltage or pressure) to increase the number of failures and, hence, to obtain reliability information more quickly. In biomedical studies the data are often obtained under different time-varying conditions and there is a problem to compare the distributions of failure time variables among several different treatment or intervention groups. To treat these data in ALT are used the so-called accelerated life models with time depending explanatory variables (stresses). The considered models are well known in reliability theory and survival analysis. They are well adapted to obtain the statistical inference in accelerated experiments with dynamic environment, when data are censored. All famous models such as Cox (proportional hazards) model, linear transformation (Dabrowska-Doksum) model, frailty model, generalized proportional model, additive hazards model, proportional hazards model, accelerated failure time model, etc…, are in the class of accelerated life models. The most famous model in ALT is the accelerated failure time (AFT) model. Here we develop a general approach for construction of the accelerated life models in accelerated experiments (in ALT) with dynamic environment, which reveals some interesting connections among many well known and new models. Keywords: accelerated life model; AFT model; arrhenius model; collapsible model; covariate; degradation model; dynamic environment; design; eyring model; linear regression model; log-linear model; meeker-Luvalle model; nonparametric model; parametric model; plan of experiment; power rule model; regression coefficients; reliability theory; sedyakin model; semiparametric model; stress; survival analysis; transformation model