Reliability of two failure mode systems subject to correlated failures

The majority of reliability modeling techniques assume systems and their components exhibit a single mode of failure. However, many systems including hardware are susceptible to two or more distinct failure modes. Previous research on two failure mode systems derived analytical expressions to determine the number of components that will maximize system reliability or minimize system cost. However, these expressions are commonly obtained from models that assume component failures are statistically independent, an assumption that is often violated in practice. This paper presents models to explicitly characterize the impact of correlated failures on the reliability and cost of several common structures. The applications of the expressions are illustrated through a series of examples, which indicate that ignoring correlation can overestimate system reliability and underestimate system cost. Thus, the expressions presented in this work can quantify the impact of correlated failure on two failure mode systems so that actions can be taken to mitigate correlation´s potentially negative influence.