Optimal System Design and Sequential Preventive Maintenance Under Uncertain Aperiodic-Changing Stresses

This paper presents a two-stage stochastic programming model with recourse for integrating the design and sequential preventive maintenance schedule of a system, which is subject to uncertain aperiodic-changing future usage stresses. Specifically, the usage stresses change as the system operates and preventive maintenance is conducted. The system undergoes imperfect repair according to the sequential preventive maintenance policy and minimal repair in response to emergency failures. The system is replaced when the maintenance is uneconomical due to the deterioration of the components. Under such future usage stresses and maintenance, this paper formulates the failure rates and lifetime distributions of components and the system, the failure rates increase with the usage stresses, and both the failure rates and usage stresses have an instantaneous incremental decrease at each preventive maintenance action. In the two-stage stochastic optimization model, the first-stage decision variables are the numbers of components to be used in the subsystems, and these variables affect the second-stage variables, which define the number of imperfect preventive maintenance actions before the replacement of the system and the aperiodic preventive maintenance time intervals for various future usage scenarios. Analytical properties about the failure rates of components and subsystems and the solution for minimizing expected system maintenance cost rate are derived. A decomposition method for solving the proposed two-stage stochastic model is designed based on the analytical results. Numerical examples and sensitivity analysis are provided for deep understanding of the proposed method.