Two-stage stochastic algorithm for system cost-reliability and maintenance optimization considering uncertain future usage scenarios

This paper develops a two-stage stochastic cost-reliability optimization model for multi-component systems subjected to uncertain stress exposure which leads to uncertain component and system degradation and wear. Optimization models are used for making decisions of system configurations to be applied in different and occasional diverse future usage scenarios. Component reliability and cost data can provide the necessary information of conditions and inputs to determine an optimum preventive maintenance policy. In this formulation, the system is exposed to distinct usage scenarios that are collectively represented as the future usage profile. This profile is described by a set of specific scenarios and their probability of occurrence or likelihood. Once these future usage profiles are known or can be estimated, the cost rate for prospective system configurations and associated maintenance can be modeled. The cost-reliability system design with maintenance modeling problem is defined as a two-stage stochastic cost-reliability programming problem with recourse. The decision variables for the first-stage are the selection of components and the number of components to be used in the system, where the cost rate objective function is constrained by component availability. The second stage variables are defined by the corrective and preventive maintenance plan in order to optimize the maintenance time interval for planned replacement of components in the system. A numerical example demonstrates that the system cost rate can be optimized by these decision variables.