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 Andreas Wilke

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


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
Pages (from-to)1622-1638
Number of pages17
JournalQuality and Reliability Engineering International
Issue number5
StatePublished - 1 Jul 2020


  • Weibull distribution
  • competing risk
  • copula
  • frailty
  • reliability


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