Misspecification of copula for one-shot devices under constant stress accelerated life-tests

Abstract

Copula models have attracted significant attention in the recent literature for modeling multivariate observations. An essential feature of copulas is that they enable us to specify the univariate marginal distributions and their joint behaviors separately. This paper provides asymptotic results for misspecification of copula models, and examines the consequences and detection of misspecification in copula models under constant-stress accelerated life-tests for one-shot devices. The one-shot device is considered as a two-component system. The reliability is an important factor in lifetime data applications, and we focus on the effect of misspecification on the estimation of the reliability of one-shot devices. Moreover, the Akaike information criterion is used as a specification test for copula model validation. A simulation study is carried out to evaluate the effect of misspecification under the Gumbel-Hougaard, the Frank and the Clayton copulas incorporated with Weibull and gamma distributions as marginal distributions, in terms of asymptotic bias, asymptotic relative bias, and root mean square error.