Renewal Decision Problem-Random Horizon
A system must operate for T units of time. T is a random variable with known distribution function F. A certain component is essential for the system's operation and when it fails must be replaced with a new component. There are n possible types of replacements. An unlimited supply of each type...
| Veröffentlicht in: | Mathematics of Operations Research. - Institute for Operations Research and the Management Sciences. - 4(1979), 3, Seite 225-232 |
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| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
1979
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| Zugriff auf das übergeordnete Werk: | Mathematics of Operations Research |
| Schlagworte: | Replacement Multiple types of replacements Exponential life-time distributions IFR horizon distribution Markov decision chains Negative dynamic programming Renewal theory Behavioral sciences Mathematics Economics |
| Zusammenfassung: | A system must operate for T units of time. T is a random variable with known distribution function F. A certain component is essential for the system's operation and when it fails must be replaced with a new component. There are n possible types of replacements. An unlimited supply of each type is assumed. A type i replacement costs <latex>$c_{i}(c_{i}>0)$</latex> and functions independently of T for an exponentially distributed length of time with rate λ <sub>i</sub>. The problem is to assign the replacements from among the various possible types so as to minimize the expected total cost of providing an operative component for the entire life of the system. The principal result of this paper, generalizing previous work where T was assumed to have a degenerate or truncated exponential distribution, is that if F is an increasing failure rate function (IFR) the optimal replacement policy has a simple intuitive interval structure. An algorithm for finding the optimal policy is indicated. Some results are obtained for the case where component life distributions are not exponential. |
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| ISSN: | 15265471 |