The optimal replacement for additive damage models in discrete setting
- 13 Downloads
A system receives shocks at successive random points of discrete time, and each shock causes a positive integer-valued random amount of damage which accumulates on the system one after another. The system is subject to failure and it fails once the total cumulative damage level first exceeds a fixed threshold. Upon failure the system must be replaced by a new and identical one and a cost is incurred. If the system is replaced before failure, a lower cost is incurred. On the basis of some assumptions, we specify a replacement rule which minimizes the long-run (expected) average cost per unit time and possesses the control limit property, Finally, an algorithm is discussed in a special case.
Key wordsIncreasing homogeneous Markov chain first failure time optimal average replacement cost optimal replacement policy λ-minimization technique compound binomial sequence
Unable to display preview. Download preview PDF.
- Posner, M.J.M., Zuckerman, D. Semi-Markov Shock Models with Additive Damage.Adv. Appl. Prob., 1986, 18: 772–790.Google Scholar
- Aven, T., Gaarder, S. Optimal Replacement in a Shock Model: Discrete Time.J. Appl. Prob., 1987, 24: 281–287.Google Scholar
- Ross, S.M. Stochastic Processes. John Wiley & Sons, 1983.Google Scholar
- Aven, T., Bergman B. Optimal Replacement Times-A General Set-up.J. Appl. Prob., 1986, 23: 432–442.Google Scholar
- Cinlar, E. Introduction to Stochastic Processes. Prentice-Hall Inc., 1975.Google Scholar
- Karlin, S., Taylor, H.M. A First Course in Stochastic Processes. Second Edition, Academic Press, 1975.Google Scholar
- Cheng, S.X. The Characterization of Binomial Sequence among Renewal Sequences.Applied Mathematics—A Journal of Chines Universities, 1992, 7: 114–128.Google Scholar
- Cheng, S.X. Pure Jump Shock Models in Discrete Time Case.J. Sys. Sic. & Math. Scis. (English Series), 1991, 4: 309–320.Google Scholar