| Title:
|
On optimal replacement policy (English) |
| Author:
|
Kasumu, Raimi Ajibola |
| Author:
|
Lešanovský, Antonín |
| Language:
|
English |
| Journal:
|
Aplikace matematiky |
| ISSN:
|
0373-6725 |
| Volume:
|
28 |
| Issue:
|
5 |
| Year:
|
1983 |
| Pages:
|
317-329 |
| Summary lang:
|
English |
| Summary lang:
|
Czech |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| Summary:
|
A system with a single activated unit which can be in $k+1$ states is considered. Inspections of the system are carried out at discrete time instants. The process of deterioration of the unit is supposed to be Markovian. The unit by its operation brings an income which is monotonically dependent on its state. A replacement of the unit is associated with certain costs. The paper gives an effective algorithm for finding the replacement strategy maximizing the average income of the system per unit time. It requests to investigate not more than $\text{log}_2$ $k$ time-stationary replacement strategies. (English) |
| Keyword:
|
replacement strategy maximizing the average income |
| Keyword:
|
time-stationary replacement strategies |
| MSC:
|
60J20 |
| MSC:
|
60K10 |
| MSC:
|
90B25 |
| idZBL:
|
Zbl 0525.60093 |
| idMR:
|
MR0712909 |
| DOI:
|
10.21136/AM.1983.104043 |
| . |
| Date available:
|
2008-05-20T18:22:56Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104043 |
| . |
| Reference:
|
[1] C. Derman: On optimal replacement rules when changes of state are markovian.in: Mathematical optimization techniques (R. Bellman ed.) Project Rand Report, April 1963. Zbl 0173.46702 |
| Reference:
|
[2] C. Derman: Finite State Markovian Decision Processes.Mathematics in Science and Engineering, vol. 67, Academic Press, New York and London (1970). Zbl 0262.90001, MR 0267686 |
| Reference:
|
[3] R. A. Kasumu: On optimal replacement policy.(1980) - unpublished. |
| Reference:
|
[4] P. Kolesar: Minimum cost replacement under markovian deterioration.Manag. Sci., vol. 12, No. 9, May (1966), 694-706. Zbl 0204.20002, MR 0195592, 10.1287/mnsc.12.9.694 |
| Reference:
|
[5] A. Lešanovský: On dependences of the expected income of a system on its initial state.to appear in IEEE Transactions on Reliability. |
| Reference:
|
[6] A. Lešanovský: On optimal replacement policy II.to appear in Proceedings of the Third Pannonian Symposium on Mathematical Statistics, Visegrád (1982). MR 0759011 |
| Reference:
|
[7] A. Lešanovský: Some remarks on the paper by P. Kolesar "Minimum cost replacement under markovian deterioration".to appear in Management Science. |
| Reference:
|
[8] A. Lešanovský: Comparison of two replacement policies.to appear in Proceedings of the Fourth Pannonian Symposium on Mathematical Statistics, Bad Tatzmannsdorf (1983). MR 0855381 |
| Reference:
|
[9] D. B. Rosenfield: Deteriorating Markov processes under uncertainty.Technical report No. 162, May (1974), Dept. of operations research and Dept. of statistics Stanford University, Stanford, California. |
| Reference:
|
[10] S. Ross: Arbitrary state markovian decision processes.Ann. Math. Stat. 39 (1968), 2118 to 2122. Zbl 0179.24704, MR 0242313, 10.1214/aoms/1177698041 |
| . |
