A Model for Censored Reliability Data with Two Dependent Failure Modes and Prediction of Future Failures

TL;DR

This paper develops a bivariate Weibull model for censored reliability data with two dependent failure modes, extending existing models, and provides methods for inference and failure prediction with practical applications.

Contribution

It introduces a new bivariate Weibull model with distinct shape parameters for dependent failure modes and develops both Bayesian and frequentist inference and prediction methods.

Findings

Monte Carlo simulations show satisfactory inference results

Bayesian and frequentist prediction methods are effective

Real data example demonstrates practical applicability

Abstract

Quite often, we observe reliability data with two failure modes that may influence each other, resulting in a setting of dependent failure modes. Here, we discuss modelling of censored reliability data with two dependent failure modes by using a bivariate Weibull model with distinct shape parameters which we construct as an extension of the well-known Marshall-Olkin bivariate exponential model in reliability. Likelihood inference for modelling censored reliability data with two dependent failure modes by using the proposed bivariate Weibull distribution with distinct shape parameters is discussed. Bayesian analysis for this issue is also discussed. Through a Monte Carlo simulation study, the proposed methods of inference are observed to provide satisfactory results. A problem of practical interest for reliability engineers is to predict field failures of units at a future time. Frequentist and Bayesian methods for prediction of future failures are developed in this setting of censored reliability data with two dependent failure modes. An illustrative example based on a real data on device failure with two failure modes is presented. The model and methodology presented in this article provide a complete and comprehensive treatment of modelling censored reliability data with two dependent failure modes, and address some practical prediction issues.