On the Properties of the Weighted Mean Residual Life in Mixtures

ABSTRACT This paper focuses on the weighted mean residual life (WMRL) in mixtures of time to failure distributions. WMRL is an aging index that accounts for transformations of nonnegative random variables. The time to failure of systems operating under changing environments is described by mixtures of distributions that capture the corresponding random effects. This study analyzes the preservation by mixtures of aging properties based on the WMRL and bending properties. The latter compare the WMRL of the mixture and the expected value of the WMRL of the distributions therein. We also analyze the combined effect of a frailty and lifetime functions in the case of mixtures following the proportional WMRL model. The results reveal the improved behavior in the WMRL of mixtures with respect to that in the sub‐populations in the mixture. This pattern is relevant for the maintenance of systems.