Abstract
As we are familiar that existence of life is uncertain. In the context of reliability and lifetime distributions, there are some measures such as the hazard rate function or the mean residual lifetime function that have been used to characterize or compare the aging process of a component. This definition deals with random variable truncated above some t, i.e. the support of the random variable is taken to be (0, t). We outline some common methods for past residual lifetime distributions with the aim to provide some insights on general construction mechanisms. Some applications are given to provide the readers a possible source of ideas to draw upon. Applications of past residual lifetime distributions in reliability, survival analysis and mortality studies are briefly discussed.
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