Optimal replacement policy for obsolete components with general failure rates
Identical components are considered, which become obsolete once new‐type ones are available, more reliable and less energy consuming. We envision different possible replacement strategies for the old‐type components by the new‐type ones: either purely preventive, where all old‐type components are re...
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Published in | Applied stochastic models in business and industry Vol. 24; no. 3; pp. 221 - 235 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Chichester, UK
John Wiley & Sons, Ltd
01.05.2008
Wiley |
Subjects | |
Online Access | Get full text |
ISSN | 1524-1904 1526-4025 |
DOI | 10.1002/asmb.706 |
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Abstract | Identical components are considered, which become obsolete once new‐type ones are available, more reliable and less energy consuming. We envision different possible replacement strategies for the old‐type components by the new‐type ones: either purely preventive, where all old‐type components are replaced as soon as the new‐type ones are available; either purely corrective, where the old‐type ones are replaced by new‐type ones only at failure; or a mixture of both strategies, where the old‐type ones are first replaced at failure by new‐type ones and next simultaneously preventively replaced after a fixed number of failed old‐type components.
To evaluate the respective value of each possible strategy, a cost function is considered, which represents the mean total cost on some finite time interval [0, t]. This function takes into account replacement costs, with economical dependence between simultaneous replacements, and also some energy consumption (and/or production) cost, with a constant rate per unit time.
A full analytical expression is provided for the cost function induced by each possible replacement strategy. The optimal strategy is derived in long‐time run. Numerical experiments conclude the paper. Copyright © 2008 John Wiley & Sons, Ltd. |
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AbstractList | Identical components are considered, which become obsolete once new‐type ones are available, more reliable and less energy consuming. We envision different possible replacement strategies for the old‐type components by the new‐type ones: either purely preventive, where all old‐type components are replaced as soon as the new‐type ones are available; either purely corrective, where the old‐type ones are replaced by new‐type ones only at failure; or a mixture of both strategies, where the old‐type ones are first replaced at failure by new‐type ones and next simultaneously preventively replaced after a fixed number of failed old‐type components.
To evaluate the respective value of each possible strategy, a cost function is considered, which represents the mean total cost on some finite time interval [0,
t
]. This function takes into account replacement costs, with economical dependence between simultaneous replacements, and also some energy consumption (and/or production) cost, with a constant rate per unit time.
A full analytical expression is provided for the cost function induced by each possible replacement strategy. The optimal strategy is derived in long‐time run. Numerical experiments conclude the paper. Copyright © 2008 John Wiley & Sons, Ltd. Identical components are considered, which become obsolete once new-type ones are available, more reliable and less energy consuming. We envision different possible replacement strategies for the old-type components by the new-type ones: either purely preventive, where all old-type components are replaced as soon as the new-type ones are available; either purely corrective, where the old-type ones are replaced by new-type ones only at failure; or a mixture of both strategies, where the old-type ones are first replaced at failure by new-type ones and next simultaneously preventively replaced after a fixed number of failed old-type components. To evaluate the respective value of each possible strategy, a cost function is considered, which represents the mean total cost on some finite time interval [0, t]. This function takes into account replacement costs, with economical dependence between simultaneous replacements, and also some energy consumption (and/or production) cost, with a constant rate per unit time. A full analytical expression is provided for the cost function induced by each possible replacement strategy. The optimal strategy is derived in long-time run. Numerical experiments conclude the paper. Copyright (C) 2008 John Wiley & Sons, Ltd. Identical components are considered, which become obsolete once new-type ones are available, more reliable and less energy consuming. We envision different possible replacement strategies for the old-type components by the new-type ones: either purely preventive, where all old-type components are replaced as soon as the new-type ones are available; either purely corrective, where the old-type ones are replaced by new-type ones only at failure; or a mixture of both strategies, where the old-type ones are first replaced at failure by new-type ones and next simultaneously preventively replaced after a fixed number of failed old-type components. To evaluate the respective value of each possible strategy, a cost function is considered, which represents the mean total cost on some finite time interval [0, t]. This function takes into account replacement costs, with economical dependence between simultaneous replacements, and also some energy consumption (and/or production) cost, with a constant rate per unit time. A full analytical expression is provided for the cost function induced by each possible replacement strategy. The optimal strategy is derived in long-time run. Numerical experiments conclude the paper. Identical components are considered, which become obsolete once new‐type ones are available, more reliable and less energy consuming. We envision different possible replacement strategies for the old‐type components by the new‐type ones: either purely preventive, where all old‐type components are replaced as soon as the new‐type ones are available; either purely corrective, where the old‐type ones are replaced by new‐type ones only at failure; or a mixture of both strategies, where the old‐type ones are first replaced at failure by new‐type ones and next simultaneously preventively replaced after a fixed number of failed old‐type components. To evaluate the respective value of each possible strategy, a cost function is considered, which represents the mean total cost on some finite time interval [0, t]. This function takes into account replacement costs, with economical dependence between simultaneous replacements, and also some energy consumption (and/or production) cost, with a constant rate per unit time. A full analytical expression is provided for the cost function induced by each possible replacement strategy. The optimal strategy is derived in long‐time run. Numerical experiments conclude the paper. Copyright © 2008 John Wiley & Sons, Ltd. |
Author | Mercier, Sophie |
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Cites_doi | 10.1287/mnsc.44.1.12 10.1023/A:1019236203575 10.1016/0377-2217(92)90026-6 10.1080/07408179408966640 10.1007/978-0-85729-410-4_496 10.1016/j.orl.2006.03.001 10.1287/mnsc.1070.0709 10.1007/s11227-006-7763-x 10.1016/0898-1221(94)00225-A 10.1002/asmb.516 10.1016/j.ejor.2005.09.043 10.1016/S0167-6377(02)00153-0 10.1016/S0167-7152(97)00068-0 10.1214/aoms/1177699149 10.1525/9780520319875-011 10.1016/0925-5273(96)80001-U 10.1016/S0377-2217(02)00651-3 10.1016/0377-2217(94)90075-2 10.1287/opre.44.1.215 10.1016/0925-5273(96)00062-X 10.1007/BF01194788 10.1002/1520-6750(198804)35:2<209::AID-NAV3220350206>3.0.CO;2-3 |
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References | Cheevaprawatdomrong T, Smith RL. A paradox in equipment replacement under technological improvement. Operations Research Letters 2003; 31(1):77-82. Dohi T, Osaki S. Optimal inventory policies under product obsolescent circumstance. Computers and Mathematics with Applications 1995; 29(3):23-30. Goldstein T, Ladany SP, Mehrez A. A discounted machine replacement model with an expected future technological breakthrough. Naval Research Logistics Quarterly 1988; 35:209-220. Mercier S, Labeau P-E. Optimal replacement policy for a series system with obsolescence. Applied Stochastic Models in Business and Industry 2004; 20(1):73-91, published online 10 February 2004. Xu SH, Li Z. Managing a single-product assemble-to-order system with technology innovations. Management Science 2007; 53(9):467-1485, published online before print 25 July 2007. Cobbaert K, Van Oudheusden D. Inventory models for fast moving spare parts subject to 'sudden death' obsolescence. International Journal of Production Economics 1996; 44(3):239-248. van Delft Ch, Vial JP. Discounted costs, obsolescence and planned stockouts with EOQ formula. International Journal of Production Economics 1996; 44:255-265. Barlow RE, Proschan F. Inequalities for linear combinations of order statistics from restricted families. Annals of Mathematical Statistics 1996; 37:1574-1592. Arnold BC, Balakrishnan N, Nagaraja HN. A First Course in Order Statistics. Wiley: New York, 1993. Hritonenkoa N, Yatsenko Y. Optimal equipment replacement without paradoxes: a continuous analysis. Operations Research Letters 2007; 35(2):245-250. Hritonenko N, Yatsenko Y. Creative destruction of computing systems: analysis and modeling. The Journal of Supercomputing 2006; 38(2):143-154. Nair SK, Hopp WJ. A model for equipment replacement due to technological obsolescence. European Journal of Operational Research 1992; 63(2):207-221. Hopp WJ, Nair SK. Markovian deterioration and technological change. IIE Transactions 1994; 26(6):74-82. Dekker R, Wildeman RE, Van Der Duyn Schouten FA. A review of multi-component maintenance models with economic dependence. Mathematical Methods of Operations Research 1997; 45(3):411-435. Chambers C. Technological advancement, learning, and the adoption of new technology. European Journal of Operational Research 2004; 152(1):226-247. Song J-S, Zipkin PH. Managing inventory with the prospect of obsolescence. Operations Research 1996; 44(1):215-222 (Special issue on New Directions in Operations Management). Ebrahimi N, Spizichino F. Some results on normalized total time on test and spacings. Statistics and Probability Letters 1997; 36(3):231-243. Mercier S. Discrete random bounds for general random variables and applications to reliability. European Journal of Operational Research 2007; 177(1):378-405, available online 15 February 2006. Jain K, Silver EA. Lot sizing for a product subject to obsolescence or perishability. European Journal of Operational Research 1994; 75(2):287-295. Rajagopalan S, Singh MR, Morton TE. Capacity expansion and replacement in growing market with uncertain technological breakthrough. Management Science 1998; 44:12-30. Mehrez A, Rabinowitz G, Shemesh E. A discrete maintenance and replacement model under technological breakthrough expectations. Annals of Operations Research 2000; 99(1-4):351-372. 2004; 20 2004; 152 2006; 38 2000; 99 1997; 36 2007; 177 1997; 45 1963 1988; 35 1994; 26 1993 1995; 29 2007; 53 1996; 37 2003; 31 2007; 35 1998; 44 1996; 44 1994; 75 1992; 63 Arnold BC (e_1_2_1_26_2) 1993 e_1_2_1_22_2 Derman C (e_1_2_1_18_2) 1963 e_1_2_1_23_2 e_1_2_1_20_2 e_1_2_1_21_2 e_1_2_1_27_2 e_1_2_1_24_2 e_1_2_1_25_2 e_1_2_1_6_2 e_1_2_1_7_2 e_1_2_1_4_2 e_1_2_1_5_2 e_1_2_1_2_2 e_1_2_1_11_2 e_1_2_1_3_2 e_1_2_1_12_2 e_1_2_1_10_2 e_1_2_1_15_2 e_1_2_1_16_2 e_1_2_1_13_2 e_1_2_1_14_2 e_1_2_1_19_2 e_1_2_1_8_2 e_1_2_1_17_2 e_1_2_1_9_2 |
References_xml | – reference: Arnold BC, Balakrishnan N, Nagaraja HN. A First Course in Order Statistics. Wiley: New York, 1993. – reference: Dekker R, Wildeman RE, Van Der Duyn Schouten FA. A review of multi-component maintenance models with economic dependence. Mathematical Methods of Operations Research 1997; 45(3):411-435. – reference: Dohi T, Osaki S. Optimal inventory policies under product obsolescent circumstance. Computers and Mathematics with Applications 1995; 29(3):23-30. – reference: Mercier S. Discrete random bounds for general random variables and applications to reliability. European Journal of Operational Research 2007; 177(1):378-405, available online 15 February 2006. – reference: Xu SH, Li Z. Managing a single-product assemble-to-order system with technology innovations. Management Science 2007; 53(9):467-1485, published online before print 25 July 2007. – reference: Nair SK, Hopp WJ. A model for equipment replacement due to technological obsolescence. European Journal of Operational Research 1992; 63(2):207-221. – reference: Cobbaert K, Van Oudheusden D. Inventory models for fast moving spare parts subject to 'sudden death' obsolescence. International Journal of Production Economics 1996; 44(3):239-248. – reference: Chambers C. Technological advancement, learning, and the adoption of new technology. European Journal of Operational Research 2004; 152(1):226-247. – reference: Hopp WJ, Nair SK. Markovian deterioration and technological change. IIE Transactions 1994; 26(6):74-82. – reference: Hritonenko N, Yatsenko Y. Creative destruction of computing systems: analysis and modeling. The Journal of Supercomputing 2006; 38(2):143-154. – reference: Mercier S, Labeau P-E. Optimal replacement policy for a series system with obsolescence. Applied Stochastic Models in Business and Industry 2004; 20(1):73-91, published online 10 February 2004. – reference: van Delft Ch, Vial JP. Discounted costs, obsolescence and planned stockouts with EOQ formula. International Journal of Production Economics 1996; 44:255-265. – reference: Barlow RE, Proschan F. Inequalities for linear combinations of order statistics from restricted families. Annals of Mathematical Statistics 1996; 37:1574-1592. – reference: Hritonenkoa N, Yatsenko Y. Optimal equipment replacement without paradoxes: a continuous analysis. Operations Research Letters 2007; 35(2):245-250. – reference: Rajagopalan S, Singh MR, Morton TE. Capacity expansion and replacement in growing market with uncertain technological breakthrough. Management Science 1998; 44:12-30. – reference: Goldstein T, Ladany SP, Mehrez A. A discounted machine replacement model with an expected future technological breakthrough. Naval Research Logistics Quarterly 1988; 35:209-220. – reference: Mehrez A, Rabinowitz G, Shemesh E. A discrete maintenance and replacement model under technological breakthrough expectations. Annals of Operations Research 2000; 99(1-4):351-372. – reference: Song J-S, Zipkin PH. Managing inventory with the prospect of obsolescence. Operations Research 1996; 44(1):215-222 (Special issue on New Directions in Operations Management). – reference: Cheevaprawatdomrong T, Smith RL. A paradox in equipment replacement under technological improvement. Operations Research Letters 2003; 31(1):77-82. – reference: Jain K, Silver EA. Lot sizing for a product subject to obsolescence or perishability. European Journal of Operational Research 1994; 75(2):287-295. – reference: Ebrahimi N, Spizichino F. Some results on normalized total time on test and spacings. Statistics and Probability Letters 1997; 36(3):231-243. – volume: 53 start-page: 467 issue: 9 year: 2007 end-page: 1485 article-title: Managing a single‐product assemble‐to‐order system with technology innovations publication-title: Management Science – start-page: 201 year: 1963 end-page: 210 – start-page: 3098 end-page: 3103 – volume: 75 start-page: 287 issue: 2 year: 1994 end-page: 295 article-title: Lot sizing for a product subject to obsolescence or perishability publication-title: European Journal of Operational Research – volume: 63 start-page: 207 issue: 2 year: 1992 end-page: 221 article-title: A model for equipment replacement due to technological obsolescence publication-title: European Journal of Operational Research – volume: 35 start-page: 245 issue: 2 year: 2007 end-page: 250 article-title: Optimal equipment replacement without paradoxes: a continuous analysis publication-title: Operations Research Letters – volume: 177 start-page: 378 issue: 1 year: 2007 end-page: 405 article-title: Discrete random bounds for general random variables and applications to reliability publication-title: European Journal of Operational Research – volume: 99 start-page: 351 issue: 1–4 year: 2000 end-page: 372 article-title: A discrete maintenance and replacement model under technological breakthrough expectations publication-title: Annals of Operations Research – volume: 152 start-page: 226 issue: 1 year: 2004 end-page: 247 article-title: Technological advancement, learning, and the adoption of new technology publication-title: European Journal of Operational Research – volume: 20 start-page: 73 issue: 1 year: 2004 end-page: 91 article-title: Optimal replacement policy for a series system with obsolescence publication-title: Applied Stochastic Models in Business and Industry – volume: 44 start-page: 12 year: 1998 end-page: 30 article-title: Capacity expansion and replacement in growing market with uncertain technological breakthrough publication-title: Management Science – volume: 44 start-page: 215 issue: 1 year: 1996 end-page: 222 article-title: Managing inventory with the prospect of obsolescence publication-title: Operations Research – volume: 26 start-page: 74 issue: 6 year: 1994 end-page: 82 article-title: Markovian deterioration and technological change publication-title: IIE Transactions – volume: 29 start-page: 23 issue: 3 year: 1995 end-page: 30 article-title: Optimal inventory policies under product obsolescent circumstance publication-title: Computers and Mathematics with Applications – start-page: 499 end-page: 506 – volume: 37 start-page: 1574 year: 1996 end-page: 1592 article-title: Inequalities for linear combinations of order statistics from restricted families publication-title: Annals of Mathematical Statistics – volume: 44 start-page: 239 issue: 3 year: 1996 end-page: 248 article-title: Inventory models for fast moving spare parts subject to ‘sudden death’ obsolescence publication-title: International Journal of Production Economics – volume: 36 start-page: 231 issue: 3 year: 1997 end-page: 243 article-title: Some results on normalized total time on test and spacings publication-title: Statistics and Probability Letters – year: 1993 – volume: 45 start-page: 411 issue: 3 year: 1997 end-page: 435 article-title: A review of multi‐component maintenance models with economic dependence publication-title: Mathematical Methods of Operations Research – volume: 31 start-page: 77 issue: 1 year: 2003 end-page: 82 article-title: A paradox in equipment replacement under technological improvement publication-title: Operations Research Letters – volume: 35 start-page: 209 year: 1988 end-page: 220 article-title: A discounted machine replacement model with an expected future technological breakthrough publication-title: Naval Research Logistics Quarterly – volume: 38 start-page: 143 issue: 2 year: 2006 end-page: 154 article-title: Creative destruction of computing systems: analysis and modeling publication-title: The Journal of Supercomputing – volume: 44 start-page: 255 year: 1996 end-page: 265 article-title: Discounted costs, obsolescence and planned stockouts with EOQ formula publication-title: International Journal of Production Economics – ident: e_1_2_1_16_2 doi: 10.1287/mnsc.44.1.12 – ident: e_1_2_1_14_2 doi: 10.1023/A:1019236203575 – ident: e_1_2_1_15_2 doi: 10.1016/0377-2217(92)90026-6 – ident: e_1_2_1_17_2 doi: 10.1080/07408179408966640 – ident: e_1_2_1_21_2 doi: 10.1007/978-0-85729-410-4_496 – ident: e_1_2_1_22_2 – ident: e_1_2_1_13_2 doi: 10.1016/j.orl.2006.03.001 – ident: e_1_2_1_8_2 doi: 10.1287/mnsc.1070.0709 – ident: e_1_2_1_12_2 doi: 10.1007/s11227-006-7763-x – ident: e_1_2_1_5_2 doi: 10.1016/0898-1221(94)00225-A – ident: e_1_2_1_20_2 doi: 10.1002/asmb.516 – ident: e_1_2_1_27_2 doi: 10.1016/j.ejor.2005.09.043 – ident: e_1_2_1_10_2 doi: 10.1016/S0167-6377(02)00153-0 – ident: e_1_2_1_25_2 doi: 10.1016/S0167-7152(97)00068-0 – ident: e_1_2_1_24_2 doi: 10.1214/aoms/1177699149 – volume-title: A First Course in Order Statistics year: 1993 ident: e_1_2_1_26_2 – start-page: 201 volume-title: Mathematical Optimization Techniques year: 1963 ident: e_1_2_1_18_2 doi: 10.1525/9780520319875-011 – ident: e_1_2_1_19_2 – ident: e_1_2_1_23_2 – ident: e_1_2_1_4_2 doi: 10.1016/0925-5273(96)80001-U – ident: e_1_2_1_9_2 doi: 10.1016/S0377-2217(02)00651-3 – ident: e_1_2_1_6_2 doi: 10.1016/0377-2217(94)90075-2 – ident: e_1_2_1_7_2 doi: 10.1287/opre.44.1.215 – ident: e_1_2_1_3_2 doi: 10.1016/0925-5273(96)00062-X – ident: e_1_2_1_2_2 doi: 10.1007/BF01194788 – ident: e_1_2_1_11_2 doi: 10.1002/1520-6750(198804)35:2<209::AID-NAV3220350206>3.0.CO;2-3 |
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Snippet | Identical components are considered, which become obsolete once new‐type ones are available, more reliable and less energy consuming. We envision different... Identical components are considered, which become obsolete once new-type ones are available, more reliable and less energy consuming. We envision different... |
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SubjectTerms | cost-based optimization order statistics preventive maintenance renewal function technological obsolescence |
Title | Optimal replacement policy for obsolete components with general failure rates |
URI | https://api.istex.fr/ark:/67375/WNG-WWSC9S5G-W/fulltext.pdf https://onlinelibrary.wiley.com/doi/abs/10.1002%2Fasmb.706 https://www.proquest.com/docview/33581887 https://hal.science/hal-00693070 |
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