Renewal Decision Problem-Random Horizon

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...

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Veröffentlicht in:Mathematics of Operations Research. - Institute for Operations Research and the Management Sciences. - 4(1979), 3, Seite 225-232
1. Verfasser: Derman, C. (VerfasserIn)
Weitere Verfasser: Smith, D. R.
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 1979
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 Applied sciences
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520 |a 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. 
540 |a Copyright 1979 The Institute of Management Sciences 
650 4 |a Replacement 
650 4 |a Multiple types of replacements 
650 4 |a Exponential life-time distributions 
650 4 |a IFR horizon distribution 
650 4 |a Markov decision chains 
650 4 |a Negative dynamic programming 
650 4 |a Renewal theory 
650 4 |a Behavioral sciences  |x Psychology  |x Cognitive psychology  |x Cognitive processes  |x Decision making  |x Optimal policy 
650 4 |a Mathematics  |x Mathematical problems  |x Boundary value problems  |x Boundary conditions 
650 4 |a Economics  |x Economic disciplines  |x Financial economics  |x Insurance  |x Insurance payouts  |x Replacement value 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Descriptive statistics  |x Statistical distributions  |x Distribution functions 
650 4 |a Economics  |x Microeconomics  |x Economic costs and benefits  |x Economic costs  |x Total costs 
650 4 |a Applied sciences  |x Computer science  |x Computer programming  |x Mathematical programming  |x Dynamic programming 
650 4 |a Mathematics  |x Pure mathematics  |x Calculus  |x Differential calculus  |x Differential equations 
650 4 |a Mathematics  |x Pure mathematics  |x Probability theory  |x Random variables 
655 4 |a research-article 
700 1 |a Smith, D. R.  |e verfasserin  |4 aut 
773 0 8 |i Enthalten in  |t Mathematics of Operations Research  |d Institute for Operations Research and the Management Sciences  |g 4(1979), 3, Seite 225-232  |w (DE-627)320435318  |w (DE-600)2004273-5  |x 15265471  |7 nnns 
773 1 8 |g volume:4  |g year:1979  |g number:3  |g pages:225-232 
856 4 0 |u https://www.jstor.org/stable/3689576  |3 Volltext 
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952 |d 4  |j 1979  |e 3  |h 225-232