SYSTEM RELIABILITY OVER AN OPERATIONAL SPECTRUM 630528
Formulas are developed for obtaining the reliability of a system or vehicle over a set of possible life histories. Difficulties in analyzing the reliability of a system are removed by considering the operational spectrum to be a weighed set of deterministic time-wise histories. With this viewpoint, it has been found previously for a simple time independent failure mode case that the life history of an element is characterized by conditions existing at the instant of minimum element reliability. This result is extended to include the cases of time dependent failure modes, multiple failure modes per element considering strength dependency, and time variable strength distributions. The last situation leads to the concept of failure condition as a generalization of the meaning of a failure mode. The collection of the conditions characterizing the life histories of the elements form a complete description of the system history. The expression for obtaining the reliability of a system over a life history from its element reliabilities appears in classical probabilistic form, without regard to the time-wise characteristics of the history. Two solutions are given for the reliability of a system over a set of histories: one exact, and the other a very useful and accurate approximation at high reliability levels.