Research On Demand And Inventory Models Of Equipment Spare Parts Based On Phase-type Distribution And Markovian Arrival Process

Nowadays, with the development of the weapon equipments, the requirements of the spare parts support become more urgent. The shortage of the spare parts would cause immeasurable military and economical loss of equipments and human lives. It is of great significance to predict the discipline of the spare parts demand effectively and make a reasonable decision on the inventory scheme for improving the reliability and safety of the equipments and reducing the cost of operation and maintenance.Based on overview of the literature on the models of the spare parts demand and inventory, considering the particularity of military equipment maintenance and spare parts management, this dissertation introduces Phase-Type(PH)distribution and Markovian Arrival Processes(MAP) to spare parts demand and inventory models that will improve the models'versatility and analytical tractability. The major contributions of this dissertation include:(1) The research on spare parts demand analytical models based on Phase-Type distributionThe existing analytical modeling methods for spare parts demand usually use exponential distribution, Weibull distribution or normal distribution for the hypothesis of random variables which leads to the inferior adaptability of models. In order to eliminate the shortcoming, the dissertation assumes that the life time, repair time, etc. of components follow PH distribution which is more suitable to describe a general distribution because of its denseness in the set of distributions defined on the nonnegative real numbers. Therefore, the models based on PH distribution will relax the random variable restriction, reduce the analytical difficulty, and enhance the calculability.According to the characteristics of military equipment maintenance and spare parts support, this part focuses on three models: the non-repairable spare parts demand model of single unit system with random shocks in organizational-level maintenance, the repairable spare parts demand model of single unit deteriorating system with replacement policy N in intermediate-level maintenance and the spare parts demand model of multi-unit system. These models are difficult for analytical modeling by other stochastic distributions except exponential distribution. This indicates that PH distribution has the same advantage as the exponential distribution. This research also formulates the disciplines of spare parts demand as a MAP, which is better form for depicting the intermittence and bursty of the spare parts demand arrival process.(2) The research on the MAP fitting approaches for spare parts demand processFor the spare parts demand forecast problems which cannot be modeled analytically, the dissertation designs a basic MAP fitting approach based on EM algorithm which enables evaluation of the parameters through spare parts demand historical data, and proposes an improved two-steps fitting algorithm based on Hyper-Erlang distribution to improve the efficiency and accuracy. This pare of research, along with the spare parts demand discipline analytical modeling based on PH distribution, construct the basis of the inventory modeling based on MAP.In order to tackle the sample-shortage problem in the process of parameter evaluation, the dissertation suggests getting the fitting samples through the simulation of the equipment operation and maintenance procedure. And in order to promote the popularity of the simulation procedure, the dissertation presents a sampling algorithm from PH distribution which can avoid the situation that several times of parameter evaluations and hypothesis testings have to be conducted on different probability distribution presumptions in the simulation process. Then, aiming at solving a significant problem, a simulation algorithm is designed to demonstrate how to generate the epoch series of spare parts demand successfully.(3) The research on spare parts inventories models based on PH distribution and MAPWhen the spare parts demand discipline is obtained by the analytical or fitting method, the dissertation studies three inventory models with PH distribution and MAP: the initial inventory model for repairable spare parts of single-unit system, the (s, S) inventories model for non-repairable spare parts and the two-echelon inventory model for repairable spare parts. In these models, repair time, replenishing time and others random varables are assumed to follow PH distribution, instead of the exponential distribution or others typical distributions; and the spare parts demand flows are described as MAP. The models take the advantages of PH distribution and MAP's versatility and effectively extend their applicability, and facilitate analysis and computation. The demonstrations of the models validate the effectivity of applying PH distribution and MAP in spart parts inventory modeling.Finally, the dissertation demonstrates the application of the methods and models mentioned above in a process that optimizes the spare parts deployment through a practical case. The result shows the correctness and practicability of the research.The modeling and analytical methods concerning equipment spare parts demand forecast and inventory management are very complicated, there still exists a lot of unsolved problems which need to be tackled by some new technologies and methodologies. The contribution in the dissertation is that some helpful discussion on developments of PH distribution and MAP for the spare parts demand and inventory models, which will strengthen spare parts supply supports and enrich equipment support theory.