Optimum Order Time for a Spare Part Inventory System Modeled by a Non-Regenerative Stochastic Petri Net

Qun JIN  Richard F. VIDALE  Yoshio SUGASAWA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E83-A   No.5   pp.818-827
Publication Date: 2000/05/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Reliability Theory and Its Applications)
Category: 
Keyword: 
maintenance,  Markov processes,  Petri nets,  optimization,  reliability,  

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Summary: 
We determine the optimum time TOPT to order a spare part for a system before the part in operation has failed. TOPT is a function of the part's failure-time distribution, the lead (delivery) time of the part, its inventory cost, and the cost of downtime while waiting delivery. The probabilities of the system's up and down states are obtained from a non-regenerative stochastic Petri net. TOPT is found by minimizing E[cost], the expected cost of inventory and downtime. Three cases are compared: 1) Exponential order and lead times, 2) Deterministic order time and exponential lead time, and 3) Deterministic order and lead times. In Case 1, it is shown analytically that, depending on the ratio of inventory to downtime costs, the optimum policy is one of three: order a spare part immediately at t = 0, wait until the part in operation fails, or order before failure at TOPT > 0. Numerical examples illustrate the three cases.