Combined Redundancy Allocation and Maintenance Planning Using a Two-Stage Stochastic Programming Model for Multiple Component Systems

A new modeling approach is presented to optimally and simultaneously design the configuration of a multicomponent system and determine a maintenance plan with uncertain future stress exposure. Traditionally, analytical models for system design and maintenance planning are applied sequentially, but this new model provides an integrated approach to make decisions considering the lifecycle cost of the system. Specifically considering the influence of uncertain future usage stresses on component and system reliability, the integrated redundancy allocation and maintenance planning problem is formulated as a two-stage stochastic programming model with recourse. In this model, the system is exposed to uncertain usage scenarios with their associated probabilities of occurrence or likelihood. The decision variables for the first stage are the selection of component types and the number of components to be used in the system, and these variables are modeled before the uncertainty is revealed. The second-stage variables, involving a recourse function, are the preventive maintenance plan, which defines optimal maintenance times for planned replacement of components under distinct usage scenarios. Numerical examples and sensitivity analysis on series–parallel systems demonstrate applications of the proposed model and provide further insights. The comparisons of the proposed integrated approach to traditional sequential method show advantages of the proposed model in cost saving.