General shock models associated with correlated renewal sequences
- 1 March 1983
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 20 (03) , 600-614
- https://doi.org/10.1017/s0021900200023858
Abstract
In this paper we define and analyze a general shock model associated with a correlated pair (Xn, Yn ) of renewal sequences, where the system fails when the magnitude of a shock exceeds (or falls below) a prespecified threshold level. Two models, depending on whether the nth shock Xn is correlated to the length Yn of the interval since the last shock, or to the length Yn of the subsequent interval until the next shock, are considered. The transform results, an exponential limit theorem, and properties of the associated renewal process of the failure times are obtained. An application in a stochastic clearing system with numerical results is also given.Keywords
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