Optimal Maintenance Decision And Joint Optimal Decision Of Maintenance And Spare Parts Inventory For Multi-unit Systems

The main reason a company keeps an inventory of spare parts is to perform maintenance in order to restore the system in such a way that it can perform its intended function. Maintenance relies on the availability of spare parts in order to reduce failure downtime and costs. The number of spare parts in inventory is determined by the maintenance demand, for each spare part. It is clear that maintenance and inventory management are strongly interconnected and should both be considered simultaneously when optimizing a company’s operations. During the past decades, most researches on joint optimization of maintenance and inventory dealt with single-unit systems. In recent years, however, increasing numbers of researchers and engineers are appreciating that, in reality, with the development of industrial technology, most machine systems have become more complex and now comprise multiple units with various dependencies. Moreover, the dependencies among the units have evolved into an essential consideration in optimal maintenance decisions, especially in joint optimal decisions of maintenance and spare parts inventory.For a system with multiple units, enumeration method is often used to analyze all possible maintenance requirements of the system. For the complexity of mathematical modeling, most of previous studies tend to develop simulation model for the system or decompose a multi-unit system into mutually influential single-unit systems. However, enumeration will be very complicated and time-consuming, even omission may occur in a system with a great number of units. Simulation model is also time-consuming and the decomposing method will injured much inaccuracy and can not get an efficient miantenance policy. In this thesis, in order to develop more efficient optimal maintenance decision models and determine the joint optimal decision of maintenance and spare parts inventory for multi-unit systems, the main studies are as follows:(1) Taking the common feature of the opportunistic maintenance models based on different maintenance strategies into account, a general deterioration state space partitioning method is presented to give an effective analysis method for modeling the optimal maintenance decision model. The representation and partition of joint deterioration state space of the system and the maintenance requirement corresponding to each space area, and their relationships are represented in the method.(2) For both multi-units systems with a known number of identical and non-identical units, the common partition models are developed using the presented deterioration state space partitioning method. All possible maintenance requirement groups at each maintenance decision time is presented, and their corresponding probabilities is deduced using the presented approach. Further, a general representation of the stationary law of the system deterioration states and its numerical solution is developed.(3) Based on the partitioning models of deterioration state space, models for the minimization of the average long-run maintenance cost rate of the general identical multi-units systems and systems with two non-identical units are developed, in which condition-based opportunistic maintenance polices are considered. Numerical experiments and sensitivity analysis are carried out to verify these models.(4) For the general identical multi-units systems, the probability of spare parts inventory state is derived considering all possible maintenance requirement groups as conditions. The probabilities of maintenance activities and spare parts ordering and holding are deduced based on it. With these probabilities, the joint optimization model of maintenance and spare parts inventory is established. Finally, a case study of a wind power farm consisting of a large number of identical components is performed.(5) For a system with two non-identical units, the stationary probability density function of the combined states with system deterioration and spare part inventory and its numerical solution is developed. Based on it, the maintenance related and spare parts related probabilities are deduced and the joint optimal decision of maintenance and spare parts inventory is determined. A case study of a wind turbines system with two key units is carried out to identify the optimal values for the parameters of the policy.