Approximations to the reliability of phased missions

A system whose configuration (block diagram or fault tree) changes during consecutive time periods (phases) performs a “phased mission.” Recently, Esary and Ziehms have shown that any multiphase mission can be transformed into an equivalent, synthetic, single‐phase system, and thus that the phased mission problem can in principle be solved by standard reliability methods. We employ these ideas here to study approximations to mission reliability and to develop an algorithm which may be of practical interest. In addition, we extend the reliability calculus of Rubinstein, and Esary and Hayne, based on an approximate hazard transform, to phased missions, and we show how this extended calculus can be used in situations where phases are not of known fixed duration.