A random review replacement model for a system subject to compound poisson shocks |
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Authors: | Y.I. Park K.C. Chae H.S. Lee |
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Affiliation: | 1. Department of Industrial Engineering , Korea Advanced Institute of Science and Technology , Taejon, 305-701, Korea;2. Department of Industrial Engineering , Kyung Hee University , Kiheung, 449-701, Korea |
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Abstract: | We present a transform–free analysis of the following model. The state of the system is initially 0 and thereafter increases jumpwise due to compound Poisson shocks. Each shock increases the state by a random amount. The system is inspected at random points in time. If the state is above a threshold at an inspection, the system is replaced, otherwise no action is taken. Each replacement instantaneously brings the state back to 0. (Existing models assume either exponential interinspection times or discrete shock magnitudes.) This model can be applied to reliability, inventory, and queueing problems.Interpretations are given throughout to make the results easier to understand and to apply |
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Keywords: | Measure-valued process Martingale problem Superprocesses Stochastic partial differential equation AMS Subject Classifications: Primary 60J60 Secondary 60G55 |
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