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

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.