Markov-chain-driven optimization of inspection-based maintenance, Part I: Models and methods

System reliability and life-cycle cost are significantly influenced by preventive maintenance (PM). PM is com-monly classified into two categories: time-based maintenance (TBM) and condition-based maintenance. Another PM approach referred to as inspection-based maintenance (IBM) incorporates condition-based activities within periodic inspections and tests. Determining the optimal maintenance rate for both TBM and IBM plans, and scheduling them effectively, poses a crucial challenge. Traditional methods assess equipment importance and condition within a reliability-centered maintenance framework. Mathematical models are commonly employed to devise robust plans, but accurate modeling based on practical conditions of the system equipment remains a key challenge. This two-part paper series introduces a novel model based on the Markov chain theory, that establishes the relationship between equipment status transition rates and the risk indices. The proposed model can be used alone or in combination with risk analysis outcomes to overcome data and budget limitations. To demonstrate its efficacy, the proposed method is implemented to optimize the PM rate of high-voltage equipment within a real-world sub-transmission substation, where the results can aid in cost estimation, equipment replacement decisions, and inventory management.