Quantitative analysis of warm standby system with N arbitrary time-to-failure distribution components

Existing analytical methods for analyzing warm standby systems are mainly Markov-based and inclusion-exclusion-based approaches. However, both approaches have their own shortcomings. As to Markov-based methods, they often confront the problem of state space explosion and require exponential components time-to-failure distributions. For the inclusion-exclusion-based approaches, the multi-integration formulas developed for quantifying minimal cut sequences generated from warm spare gate system base on exponential components time-to-failure distribution as well. In this paper, new sequential multi-integration formulas are proposed for quantifying warm spare systems, which are applicable for system having components with arbitrary time-to-failure distributions. The rigorous mathematical derivations are presented thoroughly. For a validation purpose, an illustrative example is analyzed. The results indicate that our proposed method is reasonable.