A model for failure-time data with two dependent failure modes and prediction of future failures

Abstract

Often in reliability studies we observe failure-time data with two dependent failure modes. In this article, by using a bivariate Weibull model with distinct shape parameters, we present a model for reliability data with two dependent failure modes. Inferential methods for the proposed model are discussed. The efficacy of the methods of inference is assessed through a Monte Carlo simulation study, and it is observed that the model and methods perform satisfactorily. An issue of practical interest for reliability engineers is to predict field failures at a future time. Prediction methods are developed in this setting. For illustrative purposes, analysis of a real dataset on failure of a device is presented. In summary, the model and methods presented in this article provide a comprehensive treatment for analyzing reliability data with two dependent failure modes.

Keywords:

• Bayesian analysis
• bivariate Weibull model
• dependent failure modes
• failure-time data
• likelihood analysis
• Metropolis Hastings algorithm
• prediction of future failures
• shape parameters

Acknowledgments

The authors are thankful to the anonymous reviewers for their constructive and insightful comments which helped to improve the earlier version of the manuscript significantly.

Disclosure statement

The authors report there are no competing interests to declare.

Additional information

Funding

Debanjan Mitra thanks Indian Institute of Management Udaipur for financial support to carry out this research. The research of Ayon Ganguly is supported by the Mathematical Research Impact Centric Support (File no. MTR/2017/000700) from the Science and Engineering Research Board, Department of Science and Technology, Government of India.

Notes on contributors

Aakash Agrawal

Aakash Agrawal is a Data Scientist based out of Bengaluru, Karnataka, India. He graduated with a B.Tech degree from the Indian Institute of Technology (IIT) Guwahati, in 2020. He has also been working as an independent researcher post his graduation from IIT Guwahati. He is currently interested in exploring various problems in survival analysis, including modelling dependent competing risk data.

Debanjan Mitra

Debanjan Mitra is an Associate Professor in the Quantitative Methods Division at Indian Institute of Management Udaipur, Rajasthan, India. He received his B.Sc. and M.Sc. degrees from the University of Calcutta, in 2006 and 2008, respectively. He earned his Ph.D. from McMaster University, Canada, in 2013. Areas of his research interests include models and methods for reliability and survival data, in particular, statistical analyses of truncated and censored data, competing risks data, failure-time data from reliability systems of various structures, and degradation models.

Ayon Ganguly

Ayon Ganguly is an Assistant Professor in the Department of Mathematics, Indian Institute of Technology Guwahati. He joined the department in 2016. His primary research area includes lifetime data analysis and censoring schemes. He completed his Ph.D. in Statistics from the Indian Institute of Technology Kanpur in 2013. Before joining the Indian Institute of Technology Guwahati, he taught at the Indian Institute of Information Technology Allahabad. He did post-doctoral research at the Indian Statistical Institute, Chennai, and the Department of Statistics, Savitribai Phule Pune University.