A multi-stage stochastic programming for condition-based maintenance with proportional hazards model

Condition-Based Maintenance (CBM) optimization using Proportional Hazards Model (PHM) is a kind of maintenance optimization problem in which inspections of a system relevant to its failure rate depending on the age and value of covariates are performed in time intervals. The general approach for constructing a CBM based on PHM for a system is to minimize a long run average cost per unit of time as an objective function in which the model is considered for an infinite span of time.  In this paper, a CBM model is presented based on two types of maintenance actions (minimal repair and replacement) to determine control limits to cope with the class of real-life problems in which a system would be planned for a specified planning horizon. An effective multi-stage stochastic programming approach is used to come up with the minimum expected cost given the state scenarios of the system in periods over a planning horizon. An extensive computational study is presented to demonstrate the efficiency of the proposed model through numerical instances solved by a novel hybrid meta-heuristic algorithm. A sensitivity is also performed on cost parameters to designate the effects of minimal repair cost and replacement cost in the proposed model.