Ageing Intensity Function for Conditionally Specified Models

Abstract

Jiang et al. have introduced a quantitative measure known as the ageing intensity function for evaluating the ageing properties of a component/system. The present study extends this ageing intensity function to the conditionally specified and conditional survival models. In a two component system, these two conditional ageing intensity functions provide the ageing patterns of one component when the other component has either failed or survived a specified period of time. The proposed conditionally ageing intensity function models provide simple expressions for some commonly used bivariate lifetime models. Characterization relationships are established for bivariate exponential, bivariate Weibull, conditional proportional hazards and bivariate weighted models.