A Multistate Availability Model: System Performance and Component Importance

We study a particular multistate system whose components are in one of two states - good or bad. The system state is defined to be the number of good components. An example of such a model is a power generation system consisting of n power stations. Repair is to good-asnew. A utility is assigned to the states which the system can assume, and reflects the relative value of each of the states. The performance at any time t and the steady state performance are studied by using s-expected utility. A concept of component importance is introduced which is a measure of improvement in s-expected utility of the system per unit of improvement in component availability.