Reliability Modeling and Evaluation for Discrete Competing Failure Processes

Abstract

There are many engineering systems that can fail due to both the internal degradation of the system itself and the effects of external shocks. The external shocks also affect the degradation of the system. In this paper, discrete analogues of the competing failure processes previously studied in the literature for the continuous case are considered. Exact reliability equations are obtained for a system that is exposed to both internal degradation and external shocks over periods when the shock magnitudes have a discrete probability distribution. The computationally efficient reliability equations are also presented for the particular case when the random quantities involved by the model have phase-type distributions.