Estimation of the Frank copula model for dependent competing risks in accelerated life testing

Abstract

A competing risks situation where a potential critical unit failure at random time \(X_2\) in a life test may be avoided by observing a degraded failure at some random time \(X_1\) is considered. It is thus logical to expect a dependence between the event times \(X_1\) and \(X_2\). We model the joint distribution of \(X_1\) and \(X_2\) by the Frank copula because it captures the full range of dependence and it is symmetric in its dependence structure. This paper shows how expert opinion is used to estimate the assumed Frank copula when only incomplete competing risks data are observed. Estimation of the copula allows the marginal distributions to be identified from competing risks data. Our result is thus apparent in reliability where primary interest is in the estimation of marginal failure distributions and can be extended to other applications.