Statistical Models to Analyze Failure, Wear, Fatigue, and Degradation Data with Explanatory Variables

Abstract

Failures of highly reliable units are rare. One way of obtaining a complementary reliability information is to do accelerated life testing (ALT), i.e., to use a higher level of experimental factors, hence to obtain failures quickly. Another way of obtaining complementary reliability information is to measure some parameters which characterize the aging or wear of the product in time.

Statistical inference from ALT is possible if failure time regression models relating failure time distribution with external explanatory variables (covariates, stresses) influencing the reliability are well chosen. Statistical inference from failure time-degradation data with covariates needs even more complicated models relating failure time distribution not only with external but also with internal explanatory variables (degradation, wear) which explain the state of units before the failures. In the last case, models for degradation process distribution are needed, too. In this article, we discuss the most used failure time regression models used for analysis of failure time and failure time-degradation data with covariates.

Keywords:

• Covariates
• Degradation
• Failure time regression
• Reliability
• Wear

Mathematics Subject Classification:

• Primary 62G08
• Secondary 62G20, 62F10

Acknowledgment

The authors are very grateful to three anonymous referees for numerous remarks and suggestions which helped to ameliorate substantially the article. This article was prepared with the support of StatXpert, Bordeaux, France.