Fitting the Weibull log-linear model to accelerated life-test data

TLDR

The Weibull log‑linear model is a widely used accelerated life‑test model in reliability engineering, yet its standard deviation of log(life) is often assumed constant while evidence shows it can be stress‑dependent, and existing methods frequently fail to converge and lack user‑friendly software. This paper presents an efficient algorithm to obtain the MLE of Weibull log‑linear model parameters from test data, with or without censoring, for both stress‑independent and stress‑dependent models. The algorithm performs numerical maximum likelihood estimation, handling the model’s complexity and multiple unknown parameters, and accommodates censored data. Numerical examples demonstrate the method’s validity, effectiveness, numerical stability, and ease of implementation.

Abstract

The Weibull log-linear model is a widely-used accelerated life-test model in reliability engineering. The standard deviation of log(life), s, was often assumed to be a constant or stress-independent. However, theoretical and experimental research results suggest that, in many cases, s is stress-dependent. The data analysis via the MLE method must be performed numerically, because of the complexity of the model and many unknown parameters being involved. The commonly-used methods often fail to converge when the starting point is not close to the solution, especially for censored data. Generally, no easy-to-use software is available for the Weibull log-linear model. To facilitate this process, an efficient algorithm is presented in this paper, to obtain the MLE of the model parameters from test data (with or without censoring) for both stress-independent and stress-dependent models. The validity and effectiveness of this procedure are illustrated with numerical examples. The method is numerically stable, and easy to implement and program.