Copula models for one-shot device testing data with correlated failure modes

Man Ho Alpha LING, P. S. CHAN, H. K. T. NG, N. BALAKRISHNAN

Research output: Contribution to journalArticle

Abstract

Copula models have become one of the most popular tools, especially in finance and insurance, for modeling multivariate distributions in the past few decades, and they have recently received increasing attention for data analysis in reliability engineering and survival analysis. This paper considers two Archimedean copula models — the Gumbel-Hougaard copula and Frank copula — for analyzing one-shot device data with two correlated failure modes, which are collected from constant-stress accelerated life tests. A one-shot device is a unit that cannot be used again after a test, e.g., munitions, rockets, and automobile airbags. Only either left- or right-censored data are collected instead of the actual lifetimes of the devices under test. With the aid of Kendall’s tau correlation coefficient, initial values of the dependence parameter for the copula models are presented to determine maximum likelihood estimates of model parameters through a numerical approach. Furthermore, the proposed model can be used to examine whether the correlation between times to failure modes changes over stress levels. Real data from a survival experiment are also re-analyzed to illustrate the proposed methods. Copyright © 2020 Informa UK Limited.
Original languageEnglish
JournalCommunications in Statistics - Theory and Methods
Early online date10 Feb 2020
DOIs
Publication statusE-pub ahead of print - 10 Feb 2020

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Copula Models
Failure Mode
Copula
Testing
Archimedean Copula
Accelerated Life Test
Kendall's tau
Right-censored Data
Survival Analysis
Multivariate Distribution
Automobile
Maximum Likelihood Estimate
Finance
Insurance
Correlation coefficient
Lifetime
Data analysis
Engineering
Unit
Modeling

Citation

Ling, M. H., Chan, P. S., Ng, H. K. T., & Balakrishnan, N. (2020). Copula models for one-shot device testing data with correlated failure modes. Communications in Statistics - Theory and Methods. Advance online publication. doi: 10.1080/03610926.2020.1725827

Keywords

  • Gumbel-Hougaard copula
  • Frank copula
  • Constant-stress accelerated life
  • Tests one-shot devices