A Generic Method for Modeling Accelerated Life Testing Data

Accelerated life testing (ALT) is widely used to expedite failures of a product in a short time period for predicting the product's reliability under normal operating conditions. The resulting ALT data are often characterized by a probability distribution, such as Weibull, Lognormal, Gamma distribution, along with a life-stress relationship. However, if the selected failure time distribution is not adequate in describing the ALT data, the resulting reliability prediction would be misleading. This paper proposes a generic method that assists engineers in modeling ALT data. The method uses Erlang-Coxian (EC) distributions, which belong to a particular subset of phase-type (PH) distributions, to approximate the underlying failure time distributions arbitrarily closely. To estimate the parameters of such an EC-based ALT model, two statistical inference approaches are proposed. First, the moment-matching approach (method of moments) is developed to simultaneously match the moments of the EC-based ALT model to the ALT data collected at all test stress levels. In addition, the maximum likelihood estimation (MLE) approach is proposed to handle ALT data with type-I censoring. A numerical example is provided to illustrate the capability of the generic method in modeling ALT data.