Stochastic programming on joint optimization of redundancy design and condition-based maintenance for continuously degrading systems subject to uncertain usage stresses

This study investigates the joint optimization of system redundancy design and maintenance policies under uncertain usage stresses, using various stochastic programming models and stochastic-degradation-based reliability models. It is the first to address condition-based maintenance (CBM) policies, which outperform traditional age-based maintenance by reducing over- and tardy maintenance. Three two-stage stochastic programming models are developed. The first is a risk-neutral model aiming to minimize the expected system life-cycle cost across various usage stresses. The second is a risk-averse model using conditional value-at-risk to find solutions that perform well under the worst stresses. The third model also employs a risk-averse approach, using the upper partial mean to seek robust solutions for adverse stresses. The first-stage decision variables are subsystem redundancy levels, influencing CBM policies in the second stage. These CBM decisions depend on subsystem degradation levels and usage stresses. The long-run maintenance and failure cost rate is modeled as a recourse function, affecting redundancy allocation decisions. A numerical study demonstrates that the risk-averse strategies effectively mitigate the cost of worst scenarios without significantly increasing expected system life-cycle cost over all the scenarios. The redundancy level is high under a high risk aversion and can remain stable in a certain range of risk aversion. When the risk aversion is minor and the primary goal is the lowest expected lifetime-cycle cost, the redundancy design from risk-neutral model is preferred. The two risk-averse models would not generate the same redundancy design, no matter how to adjust the risk-averse parameters in the two models. Thus, the two risk-averse methods cannot be used exchangeable. The model using conditional value-at-risk is suitable for the cases where severe usage stresses could happen and the bad consequence cannot be tolerated. The model with upper partial mean is good for stabilizing the performances under all the adverse scenarios.