Use-level lifetime distribution estimation under dependent right censored test data

Abstract

Accelerated life testing (ALT) is a practice for estimating unit reliability at normal use conditions using failure data obtained under more severe test conditions. We focus on life tests where a potential critical unit failure at X2 (unit lifetime) may be avoided by a degraded failure at some random time X1. Degraded and critical failures are linked through the degradation process,
hence the situation under consideration is that of dependent competing risks. We apply the general result that if the copula C(.; .) of (X1; X2) is known, competing risks data uniquely determine the marginal distributions at each stress level. Interest here (and in life testing studies in general) is in unit lifetime. Accordingly, our target of estimation is to extrapolate a use-level lifetime distribution from which important reliability measures such as mean lifetime, warranty period among others are derived. The paper is based in part on a PhD thesis by Hove (2014).