A chance-constrained net revenue model for online dynamic predictive maintenance decision-making

Most models for predictive maintenance (PdM) decision-making focus on the expected value of a system performance metric (e.g., the expected cost rate). However, focusing solely on such expected values may overlook the significant risks of resulting PdM decisions. Indeed, it would be practically valuable to make the optimal PdM decision by considering the least probability of achieving a target system performance. Furthermore, emphasizing only maintenance costs without accounting for operational revenues can render the maintenance strategies unappealing, particularly when the revenues across system lifecycles are significant. This study introduces a method that employs a stochastic net revenue model and chance-constrained programming to address these issues in PdM decision-making, wherein the preventive maintenance cost is proportional to the system's current degradation state. By exemplifying system degradation with the Gamma process, we derive the probability density function of stochastic net revenue and present a Bayesian method to simultaneously update the drift and diffusion parameters of the Gamma process model. The effectiveness and practical applicability of our proposed chance-constrained net revenue model and parameter updating method are demonstrated through a numerical example and a case study.