Likelihood‐based Inference for a Frailty‐copula Model Based on Competing Risks Failure Time Data

Yin‐Chen Wang, Takeshi Emura*, Tsai‐Hung Fan, Simon M.S. Lo, Ralf Wilke

*Corresponding author for this work

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A competing risks phenomenon arises in industrial life tests, where multiple types of failure determine the working duration of a unit. To model dependence among marginal failure times, copula models and frailty models have been developed for competing risks failure time data. In this paper, we propose a frailty‐copula model, which is a hybrid model including both a frailty term (for heterogeneity among units) and a copula function (for dependence between failure times). We focus on models that are useful to investigate the reliability of marginal failure times that are Weibull distributed. Furthermore, we develop likelihood‐based inference methods based on competing risks data, including accelerated failure time models. We also develop a model‐diagnostic procedure to assess the adequacy of the proposed model to a given dataset. Simulations are conducted to demonstrate the operational performance of the proposed methods, and a real dataset is analyzed for illustration. We make an R package “gammaGumbel” such that users can apply the suggested statistical methods to their data.
Original languageEnglish
JournalQuality and Reliability Engineering International
Issue number5
Pages (from-to)1622-1638
Number of pages17
Publication statusPublished - Jul 2020

Bibliographical note

Published online: 11. May 2020


  • Competing risk
  • Copula
  • Frailty
  • Reliability
  • Weibull distribution

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