2009•Systems Engineering - Theory & PracticeRequires access

Spare parts(s,S)inventories system based on Phase-type distribution and Markovian arrival process

Guo Bo

Abstract

This paper investigated the system that consists of several same items,and assumed the life time,replacement repair time of items and the replenishing time follow the continuous time Phase-type(PH) distribution,instead of the exponential distribution or others typical distributions.Then it was proven that the spare parts demand process is a Markovian arrival process(MAP).Based on this conclusion,this paper studied the(s,S) inventories model,and got the distributions and the parameters of the first order time, cycle time and stock out time about this inventories system.Finally,a numerical example was given to illustrate the effectiveness of the model.

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Key concepts: Phase-type distribution, Spare part, Markovian arrival process, Exponential distribution, Markov process, Computer science, Process (computing), Distribution (mathematics)