Joint modeling of linear degradation and failure time data with masked causes of failure under simple step-stress test

Abstract

In this paper, we propose a method to model the relationship between degradation and failure time for a simple step-stress test where the underlying degradation path is linear and different causes of failure are possible. It is assumed that the intensity function depends only on the degradation value. No assumptions are made about the distribution of the failure times. A simple step-stress test is used to induce failure experimentally and a tampered failure rate model is proposed to describe the effect of the changing stress on the intensities. We assume that some of the products that fail during the test have a cause of failure that is only known to belong to a certain subset of all possible failures. This case is known as masking. In the presence of masking, the maximum likelihood estimates of the model parameters are obtained through the expectation–maximization algorithm by treating the causes of failure as missing values. The effect of incomplete information on the estimation of parameters is studied through a Monte-Carlo simulation. Finally, a real-world example is analysed to illustrate the application of the proposed methods.

Keywords:

• Expectation–maximization algorithm
• cause of failure
• intensity
• linear degradation path
• masked data
• reliability function

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by University of Tehran [268235/1/07]. The authors advise no direct funding is associated with the research reported in this article.