In maintenance practice, there is such a situation where the spare parts replacement should be carried out at the scheduling time of calendar or usage for whichever comes first. The issue of two-dimensional preventive maintenance usually was not addressed by traditional methods, and at present, few studies were focused on this very topic. Based on these considerations, this paper presented the two-dimensional preventive policy where replacements of spare parts are based on both calendar time and usage time. A novel model was developed to forecast spare parts demands under two-dimensional preventive maintenance policy, and a discrete algorithm was presented for solving the mathematical model. A case study was given to demonstrate its applicability and validity, and it was showed that the presented model can be used to forecast spare parts demands as well as to optimize spare parts and preventive maintenance jointly.

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The multi-strategy improved sparrow search algorithm (MSISSA) is proposed to address the problems that the sparrow search algorithm (SSA) is not rich in population diversity, and is prone to fall into local optimality and poor accuracy in solving multi-dimensional functions. Firstly, Cat mapping is used to initialize the SSA population. Secondly, an elite reverse learning strategy is introduced to increase the population diversity and improve the global search ability of SSA. Then, the number of discoverers and the number of aware-at-risk sparrows are dynamically adjusted by improving the scaling factor. Finally, individuals are subjected to Cauchy variation or Tent chaos perturbation according to their fitness values to effectively solve the problem of their falling into local optimality. Simulation results show that MSISSA has higher performance in finding the optimum compared with classical optimization algorithms such as SSA.

As a new form of support contract, performance-based contracting has been extensively applied in both public and private sectors. However, maintenance policies under performance-based contracting have not gotten enough attention. In this paper, a preventive maintenance optimization model based on three-stage failure process for a single-component system is investigated with an objective of maximizing the profit and improving system performance at a lower cost under performance-based contracting. Different from conventional optimization models, the step revenue function is used to correlate profit with availability and cost. Then, a maintenance optimization model is proposed to maximize profit by optimizing the inspection interval. Moreover, the customers’ upper limit of funds is considered when we use the revenue function, which has rarely been considered in past studies. Finally, a case study on the cold water pumps along with comparison of linear and step revenue function and sensitivity analysis is provided to illustrate the applicability and effectiveness of our proposed approach.

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