On compact modeling of coupling effects in maintenance processes of complex systems

While the complexity of modern engineering systems is significantly mitigated by modularization, the number of modules (e.g., line-replaceable units) can still be large enough to pose a challenge of developing a coordinated maintenance policy that accounts for the coupling among individual maintenance schedules for each module. This paper focuses on opportunistic maintenance, induced failure, and other coupling mechanisms caused by competing risk phenomena. Modeling the maintenance process of an individual module or component, even if it includes modern condition-based considerations, can be described by a relatively small number of distinct states. In contrast, creating a system-level model that captures all relevant coupling leads to a state-space explosion; an implementation of such models is either very expensive or not feasible at all. To address this issue, the present paper explores the idea of developing component-level models that incorporate the aggregate effects of other components by providing a compact statistical representation of the combined influence on a given component of all other system components. This approach is somewhat analogous to the mean-field theory used in physics to avoid explicit description of pair-wise interactions. An analytical method based on asymptotic considerations is developed for combining the effects of multiple components into a single Weibull distribution (inspection intervals are assumed to be smaller than the failure scale). The accuracy of this approach is demonstrated by successfully representing the combined effect of two competing Weibull distributions as well as the combined effect of two competing lognormal distributions. In particular, it is shown that the proposed method provides a superior match for the combined distribution in the relevant time range as compared to standard methods of approximating a distribution (e.g., matching moments or using the maximum likelihood estimate). The accuracy of representing opportunities using exponential distributions is explored as well.