Derivation of Reliability and Variance Estimates for Multi-State Systems With Binary-Capacitated Components

This paper analytically derives the system reliability estimate, and the associated variance estimate for multi-state systems respectively using reliability, and variance estimates of binary-capacitated components. The derivation utilizes the universal generating function method to formulate a state table and a product expectation table when replacing two components with an equivalent virtual component. Closed-form expressions of the system reliability estimate and the associated variance estimate are formulated through an iterative derivation process. The derivation can be applied to multi-state systems with series-parallel configurations. Three example systems in the literature are used to illustrate the effectiveness and accuracy of the proposed analytical estimation approach. The confidence interval for the system reliability estimate is developed based on the derived results. The developed interval is then compared with another interval from the literature that approximated the variance estimate using a pseudo binomial distribution. Comparisons through Monte Carlo simulations on the example systems indicate that the coverage probabilities have been significantly improved by the interval constructed based on the proposed derivation.