Joint redundancy and maintenance optimization for multistate series–parallel systems

This paper formulates the joint redundancy and replacement schedule optimization problem generalized to multistate system, where the system and its components have a range of performance levels. Multistate system reliability is defined as the ability to maintain a specified performance level. The system elements are chosen from a list of available products on the market and the number of such elements is determined for each system component. Each element is characterized by its capacity, reliability and cost. The reliability of a system element is characterized by its lifetime distribution with the hazard rate, which increases with time. It is specified as the expected number of failures during different time intervals. The optimal system structure and the number of element replacements during the study period are defined as those which provide the desired level of system reliability with minimal sum of costs of capital investments, maintenance and unsupplied demand caused by failures. A universal generating function technique is applied to evaluate the multistate system reliability. A genetic algorithm is used as an optimization technique. Examples of determination of the optimal system structure and replacement schedule are provided.