General shock models associated with correlated renewal sequences
- 1 September 1983
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 20 (3) , 600-614
- https://doi.org/10.2307/3213896
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
This publication has 12 references indexed in Scilit:
- Generalized Poisson Shock ModelsThe Annals of Probability, 1981
- On Level Crossing Analysis of QueuesAustralian Journal of Statistics, 1981
- Some analyses on the control of queues using level crossings of regenerative processesJournal of Applied Probability, 1980
- Semi-stationary clearing processesStochastic Processes and their Applications, 1978
- On up- and downcrossingsJournal of Applied Probability, 1977
- Cost Models for Stochastic Clearing SystemsOperations Research, 1977
- Stochastic clearing systemsStochastic Processes and their Applications, 1974
- Shock Models and Wear ProcessesThe Annals of Probability, 1973
- Reliability Applications of a Bivariate Exponential DistributionOperations Research, 1968
- Random Hazard in Reliability ProblemsTechnometrics, 1963