Abstract
The purpose of this paper is to analyze systems composed of several parts, at different working levels. At time t, only the performance level of the system, exactly determined in an additive way by the level of the unobservable components, can be observed. We obtain the probability distribution of the component state vector, given the system performance level observed, under the asumption that each component spends an exponential time in each state. Because of their complexity, these distributions, in practice, cannot be directly evaluated. Therefore, we provide some recurrent methods which allow us to calculate those probabilities in polynomial time. Finally, the question of using these results to obtain an optimal replacement policy is considered.
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References
E. El-Neweihi and F. Proschan, Degradable systems: A survey of multistate coherent systems, Communications in Statistic-Theory Math. 13(1984)405-432.
B. Natvig and E. Funnemark, Multistate coherent systems, in: Encyclopedia of Statistical Sciences, Vol. 5, eds. S. Kotz and N.L. Johnson, Wiley, 1985.
C. Derman, On optimal replacement rules when changes of states are Markovian, in: Mathematical Optimization Techniques, ed. R. Bellman, University of California Press, Berkeley, CA, 1963.
P. Kolesar, Minimum cost replacement under Markovian deteroration, Management Science 12(1966)694-706.
B. Kalymon, Machine replacement with stochastic costs, Management Science 18(1972)288-298.
E.P.C. Kao, Optimal replacement problem rules when changes of states are semi-Markovian, Operations Research 21(1973)1231-1249.
M. Ohnishi, Z-M. Zou, T. Ibaraki and H. Mine, An optimal replacement problem of a semi-Markovian deteriorating system, Memories of the Engineering Kyoto University 48(1986)344-358.
K.C. So, Optimality of control limit policies in replacement models, Naval Research Logistics 39(1992)685-697.
G.E. Monahan, A survey of partially observable Markov decision processess: Theory, models and algorithms, Management Science 28(1982)1-16.
C.C. White, A survey of solution techniques for the partially observable Markov decision process, Annals of Operations Research 32(1991)215-230.
R.D. Smallwood and E.J. Sondik, The optimal control of partially observable Markov decision processess over a finite horizon, Operations Research 21(1973)1071-1088.
Y. Serin, A nonlinear programming model for partially observable Markov decision processess: Finite horizon case, European Journal of Operational Research 86(1996)549-564.
E.J. Sondik, The optimal control of partially observable Markov decision processess over the infinite horizon: Discounted cost case, Operations Research 26(1978)282-304.
C.C. White and W.T. Scherer, Solution procedures for partially observed Markov decision processess, Operations Research 37(1989)791-797.
Z. Sinuany-Stern, Replacement policy under partially observed Markov process, International Journal of Production Economics 29(1993)159-166.
S.M. Ross, Stochastic Processes, Wiley, 1983.
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Mallor, Azcárate On replacement policies for additive systemswith several working levels. Annals of Operations Research 91, 63–82 (1999). https://doi.org/10.1023/A:1018918311166
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DOI: https://doi.org/10.1023/A:1018918311166