New formula for the failure/repair frequency of multi-state monotone systems and its applications

The paper deals with calculation methods for failure and repair frequencies of multi-state monotone systems, both for the instantaneous and steady state cases. First, the fixed demand is considered. Based on the binary representation of multi-state structure, we have obtained a new formula for the failure/repair frequency. This formula is used to derive simple rules for the calculation of failure/repair frequency. These rules show how to convert an expression for the system availability into appropriate expression for the system failure/repair frequency. The applicability of the rules is illustrated by some examples. Finally, expressions for the failure/repair frequency for systems operating under random demand are obtained. Since both input and output data have similar format, the rules can be used in a recursive manner, allowing easy analysis of complex systems with hierarchical structure.