Characteristic functions of stochastic integrals and reliability theory

This paper concerns reliability theoretic problems involving systems of n components subject to stochastic hazard rates with independent increments. General methods are given for finding the probabilities of service at specified times and the joint characteristic function of the system failure time and the component hazard rates at the time of failure. These methods involve evaluation of integrals of the form magnified image where u′ is an n‐component row vector, W(t) is an n by n matrix, and X(t) is an n‐component stochastic process with independent increments and X(0) = 0. Some illustrative applications to one component systems and multicomponents systems in series and in parallel are presented.