Abstract
In this article, the mean lifetime of an individual whose lives lost based on a function of the time before which the individual has passed away is considered. The measure is used to construct a semi‐parametric model called proportional mean departure time model. Examples are given and evidences are gathered to show that the model is a proper alternative for the proportional mean past lifetime model. Closure properties of the model concerning several stochastic orders and a number of reliability properties are established. Finally, the model is extended to entertain random amounts of the parameter and establish a proportional mean departure time frailty model. Further stochastic properties using several stochastic orders are developed in the context of the frailty model.
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