System reliability modeling considering the dependence of component environmental influences

A system reliability modeling procedure is described and demonstrated to accommodate the case when component failure times are statistically correlated because of the shared environmental exposure of components within a system. When component failure times are correlated, independence assumptions are not valid, and thus, many common reliability modeling practices are inappropriate. If component reliability is influenced by environmental exposure, then the components within a system are likely to have correlated time-to-failures because all components within a system are influenced similarly by the system-level environmental stress profile. This scenario is often overlooked when failure data is analyzed for a homogeneous population of parts that have experienced nonhomogeneous usage profiles. The model presented here is based on proportional hazards models for component reliability and a discretized approximation of the joint probability density function for system environmental stress variables. The discretization approach is mathematically convenient, accurate and offers several pragmatic advantages over alternative computation approaches. A hypothetical three-component series system is analyzed, and the results are compared to two common approximations: (I)component independence assumption and (2) use of environmental stress average values. The results indicate that the described approach is convenient and has the potential to be scaled-up to large problems.