Hierarchical Variance Decomposition of System Reliability Estimates With Duplicated Components

A hierarchical decomposition procedure is proposed to determine the variance of the reliability estimate for complex systems with duplicated components. For these systems, multiple copies of the same component type are used within the system, but only a single reliability estimate is available for each distinct component type. The variance of the reliability estimate is magnified at the system-level due to the covariance of component reliability estimates. Estimating the covariance becomes a formidable task if the system structure is complicated. A hierarchical model is proposed to decompose the system reliability estimate into component levels through intermediate layers. The decomposition procedure causes reliability estimates of duplicated components to remain s-independent when computing the associated variance on the adjacent upper layer. The first order Taylor series expansion is used to propagate the variance from the component level to the system level via intermediate layers. The hierarchical decomposition is preferable for designing robust, reliable systems by reducing or minimizing the system reliability variance at the component level.