The integrated importance measure of multi-state compound systems for maintenance processes

Based on the integrated importance measure (IIM), the IIM of parallel-series and series-parallel systems for maintenance process is generalized, and some properties of the generalized IIM are discussed. Under the assumption that the states transition process of component in a system is an irreducible continuous-time Markov chain, equivalent formulas of IIM are obtained for parallel-series and series-parallel systems, and the time complexity of the general IIM is decreased from O(n²) to O(n) or O(1). At last, an numerical example demonstrates the generalized IIM in multi-state compound systems, and verifies the consistency of the IIM and its equivalent formulas.