Reliability of coherent systems whose operating life is defined by the lifetime and power of the components

Abstract: We consider systems whose lifetime is measured by the time of physical degradation of components, as well as the degree of power each component contributes to the system. The lifetimes of the components of the system are random variables. The power that each component contributes to the system is the product of a random variable and a time-decreasing stable function. The operational reliability of these systems is investigated and shown that it is determined by the joint lifetime functions of the order statistics and their concomitants. In addition to general formulas, examples are given using some known life distributions, and graphs of the operation life functions are shown.