Optimizing Dynamic Performance of Multistate Systems With Heterogeneous 1-Out-of- ${N}$ Warm Standby Components

This paper models and optimizes dynamic performance of multistate systems with a general series parallel structure. Each system component is a 1-out-of-N warm standby configuration of heterogeneous functional elements, which can be characterized by different time-to-failure distributions, performances, and costs. The entire system must satisfy a random demand specified by a time-dependent distribution. An iterative algorithm is developed for determining performance stochastic processes of particular components. A universal generating function technique is used for evaluating expected system availability and unsupplied demand over a particular mission time for the considered system. Two types of optimization problems are then identified and solved, with the objective of finding component structures and element activation sequences to maximize system availability, or minimize unsupplied system demand, or minimize total cost. Optimization results can facilitate the optimal decision on design and operation of multistate series parallel systems. A practical example of a power station coal transportation system is provided to illustrate application of the proposed methodology and optimization problems.