Abstract
When systems are subjected to both chance and wear-out failures, the mean of the failure distribution—which would be the average life of the system—does not exist in closed form. In this article, such a distribution is developed from basic engineering phenomena; its general mean is developed in nonclosed form; a particular solution easier to evaluate is derived, and the attention of the researchers in “equipment life”, “reliability”, and “maintenance” as well as in statistics and mathematics is drawn toward developing the relevant integral transform for this function. Some related distributions depicting various combinations of chance failures, wear-out failures, and aging and standby processes are also discussed.
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