Properties of the Weibull cumulative exposure model

TL;DR

This paper investigates properties of the Weibull cumulative exposure model in accelerated life testing, highlighting the importance of the shape parameter and demonstrating model validation through maximum likelihood estimation on cable failure data.

Contribution

It analyzes the Weibull cumulative exposure model's properties, emphasizing the necessity of a shape parameter greater than 1 and illustrating model validation with real data.

Findings

Shape parameter must be larger than 1 for accurate modeling.

Average and standard deviation depend on model parameters.

Maximum likelihood estimation can validate the model on real data.

Abstract

This article is aimed at the investigation of some properties of the Weibull cumulative exposure model on multiple-step step-stress accelerated life test data. Although the model includes a probabilistic idea of Miner's rule in order to express the effect of cumulative damage in fatigue, our result shows that the application of only this is not sufficient to express degradation of specimens and the shape parameter must be larger than 1. For a random variable obeying the model, its average and standard deviation are investigated on a various sets of parameter values. In addition, a way of checking the validity of the model is illustrated through an example of the maximum likelihood estimation on an actual data set, which is about time to breakdown of cross-linked polyethylene-insulated cables.