Two approximations of renewal function for any arbitrary lifetime distribution
The renewal functions (RFs) of most distribution functions do not have closed-form expressions while such expressions are desired for the optimization problems involved RF. Many efforts have been made to develop approximations of RF. However, it seems that no RF approximation is accurate enough in t...
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| Vydané v: | Annals of operations research Ročník 311; číslo 1; s. 151 - 165 |
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| Médium: | Journal Article |
| Jazyk: | English |
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New York
Springer US
01.04.2022
Springer Springer Nature B.V |
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| ISSN: | 0254-5330, 1572-9338 |
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| Abstract | The renewal functions (RFs) of most distribution functions do not have closed-form expressions while such expressions are desired for the optimization problems involved RF. Many efforts have been made to develop approximations of RF. However, it seems that no RF approximation is accurate enough in the entire time range. In this paper, we propose two RF approximations. The first approximation is obtained through smoothly connecting two limiting relations and fairly accurate in the entire time range. The second approximation has the same function form as the first part of the first approximation but the model parameter is determined in a different way so as to achieve higher accuracy for small to moderate time range. The expressions of the proposed approximations are simple and applicable for any arbitrary lifetime distribution. Their accuracy is analyzed and, the appropriateness and usefulness are illustrated by a numerical example. |
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| AbstractList | The renewal functions (RFs) of most distribution functions do not have closed-form expressions while such expressions are desired for the optimization problems involved RF. Many efforts have been made to develop approximations of RF. However, it seems that no RF approximation is accurate enough in the entire time range. In this paper, we propose two RF approximations. The first approximation is obtained through smoothly connecting two limiting relations and fairly accurate in the entire time range. The second approximation has the same function form as the first part of the first approximation but the model parameter is determined in a different way so as to achieve higher accuracy for small to moderate time range. The expressions of the proposed approximations are simple and applicable for any arbitrary lifetime distribution. Their accuracy is analyzed and, the appropriateness and usefulness are illustrated by a numerical example. |
| Audience | Academic |
| Author | Jiang, R. |
| Author_xml | – sequence: 1 givenname: R. orcidid: 0000-0002-4688-5065 surname: Jiang fullname: Jiang, R. email: jiang@csust.edu.cn organization: School of Automotive and Mechanical Engineering, Changsha University of Science and Technology |
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| CitedBy_id | crossref_primary_10_1007_s11009_024_10088_9 crossref_primary_10_1016_j_ress_2023_109137 crossref_primary_10_1007_s11009_022_09953_2 crossref_primary_10_1007_s11009_023_09995_0 crossref_primary_10_1007_s00184_024_00977_x crossref_primary_10_1080_02331888_2024_2406564 crossref_primary_10_1007_s11009_024_10075_0 crossref_primary_10_1080_08982112_2020_1747628 crossref_primary_10_1109_TR_2023_3347269 |
| Cites_doi | 10.1007/978-1-4615-4655-9 10.1109/24.52614 10.1016/j.ress.2018.07.030 10.1109/24.784278 10.1016/S0304-4149(97)00045-8 10.1007/s11009-008-9098-y 10.1109/24.690909 10.1081/SAC-100001862 10.1016/j.ress.2010.04.007 10.1016/j.cie.2004.07.009 10.1081/STA-120028689 10.1080/03610910802440327 10.1016/j.ress.2007.03.026 10.1057/jors.1995.183 10.1080/07408179508936750 10.1080/07408170701487989 10.1007/978-0-85729-215-5_9 10.1016/j.cor.2014.10.017 10.1016/j.probengmech.2014.09.004 10.1081/SAC-120013107 10.1016/j.ijpe.2013.06.016 10.1080/03610918908812760 10.1016/S0167-9473(96)00052-7 10.1007/978-3-662-47215-6_16 10.1016/0026-2714(89)90012-7 10.1080/16843703.2015.11673431 10.1007/978-3-540-24808-8_1 |
| ContentType | Journal Article |
| Copyright | Springer Science+Business Media, LLC, part of Springer Nature 2019 COPYRIGHT 2022 Springer Annals of Operations Research is a copyright of Springer, (2019). All Rights Reserved. Springer Science+Business Media, LLC, part of Springer Nature 2019. |
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| DOI | 10.1007/s10479-019-03356-2 |
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| References | Ayhan, Limon-Robles, Wortman (CR1) 1999; 48 Zacks (CR29) 2010; 12 Brezavšček (CR3) 2016; 12 Chaudhry (CR5) 1995; 46 Jiang (CR14) 2008; 93 Gertsbakh, Shpungin (CR12) 2004; 33 Çetinkaya, Tekin, Lee (CR4) 2008; 40 Smeitink, Dekker (CR26) 1990; 39 From (CR10) 2001; 30 Jiang (CR16) 2015 Rao (CR23) 1995; 27 Parsa, Jin (CR22) 2013; 146 Blischke, Murthy (CR2) 2003 Daley, Vesilo (CR8) 1997; 70 CR9 Spearman (CR27) 1989; 29 Jiang, Murthy (CR18) 2008 Jiang (CR15) 2010; 95 Lin, Shue (CR21) 2005; 48 Cui, Xie (CR7) 2003; 32 Xie (CR28) 1989; 18 Ghodrati, Tadj (CR13) 2011 Jin, Gonigunta (CR19) 2009; 38 Kumar, Crocker, Knezevic, El-Haram (CR20) 2000 Riascos-Ocho, Sanchez-Silva, Akhavan-Tabatabaei (CR24) 2014; 38 Samanta, Chaudhry, Pacheco, Gupta (CR25) 2015; 56 Garg, Kalagnanam (CR11) 1998; 47 Constantine, Robinson (CR6) 1997; 24 Jiang (CR17) 2018; 180 R Jiang (3356_CR16) 2015 B Ghodrati (3356_CR13) 2011 AG Constantine (3356_CR6) 1997; 24 SK Samanta (3356_CR25) 2015; 56 A Brezavšček (3356_CR3) 2016; 12 H Ayhan (3356_CR1) 1999; 48 ML Chaudhry (3356_CR5) 1995; 46 R Jiang (3356_CR17) 2018; 180 R Jiang (3356_CR15) 2010; 95 BM Rao (3356_CR23) 1995; 27 R Jiang (3356_CR18) 2008 M Xie (3356_CR28) 1989; 18 H Parsa (3356_CR22) 2013; 146 3356_CR9 S Çetinkaya (3356_CR4) 2008; 40 I Gertsbakh (3356_CR12) 2004; 33 WP Blischke (3356_CR2) 2003 DJ Daley (3356_CR8) 1997; 70 R Jiang (3356_CR14) 2008; 93 A Garg (3356_CR11) 1998; 47 PC Lin (3356_CR21) 2005; 48 S Zacks (3356_CR29) 2010; 12 L Cui (3356_CR7) 2003; 32 J Riascos-Ocho (3356_CR24) 2014; 38 SG From (3356_CR10) 2001; 30 T Jin (3356_CR19) 2009; 38 UD Kumar (3356_CR20) 2000 ML Spearman (3356_CR27) 1989; 29 E Smeitink (3356_CR26) 1990; 39 |
| References_xml | – year: 2000 ident: CR20 publication-title: Reliability, maintenance and logistic support: A life cycle approach doi: 10.1007/978-1-4615-4655-9 – volume: 39 start-page: 71 issue: 1 year: 1990 end-page: 75 ident: CR26 article-title: A simple approximation to the renewal function publication-title: IEEE Transactions on Reliability doi: 10.1109/24.52614 – volume: 180 start-page: 302 year: 2018 end-page: 311 ident: CR17 article-title: Performance evaluation of seven optimization models of age replacement policy publication-title: Reliability Engineering and System Safety doi: 10.1016/j.ress.2018.07.030 – volume: 48 start-page: 82 issue: 2 year: 1999 end-page: 188 ident: CR1 article-title: Approach for computing tight numerical bounds on renewal functions publication-title: IEEE Transactions on Reliability doi: 10.1109/24.784278 – volume: 70 start-page: 265 issue: 2 year: 1997 end-page: 282 ident: CR8 article-title: Long range dependence of point processes, with queueing examples publication-title: Stochastic Processes and their Applications doi: 10.1016/S0304-4149(97)00045-8 – volume: 12 start-page: 555 issue: 4 year: 2010 end-page: 565 ident: CR29 article-title: The availability and hazard of a system under a cumulative damage process with replacements publication-title: Methodology and Computing in Applied Probability doi: 10.1007/s11009-008-9098-y – volume: 47 start-page: 66 issue: 1 year: 1998 end-page: 72 ident: CR11 article-title: Approximations for the renewal function publication-title: IEEE Transactions on Reliability doi: 10.1109/24.690909 – volume: 30 start-page: 113 issue: 1 year: 2001 end-page: 128 ident: CR10 article-title: Some new approximations for the renewal function publication-title: Communications in Statistics-Simulation and Computation doi: 10.1081/SAC-100001862 – volume: 95 start-page: 963 issue: 9 year: 2010 end-page: 969 ident: CR15 article-title: A simple approximation for the renewal function with an increasing failure rate publication-title: Reliability Engineering and System Safety doi: 10.1016/j.ress.2010.04.007 – volume: 48 start-page: 69 issue: 1 year: 2005 end-page: 82 ident: CR21 article-title: Application of optimal control theory to product pricing and warranty with free replacement under the influence of basic lifetime distributions publication-title: Computers & Industrial Engineering doi: 10.1016/j.cie.2004.07.009 – volume: 33 start-page: 639 issue: 3 year: 2004 end-page: 649 ident: CR12 article-title: Renewal function and interval availability: A numerical Monte–Carlo study publication-title: Communications in Statistics. Theory and Methods doi: 10.1081/STA-120028689 – volume: 38 start-page: 154 issue: 1 year: 2009 end-page: 171 ident: CR19 article-title: Weibull and gamma renewal approximation using generalized exponential functions publication-title: Communications in Statistics: Simulation and Computation doi: 10.1080/03610910802440327 – volume: 93 start-page: 616 issue: 4 year: 2008 end-page: 626 ident: CR14 article-title: A Gamma–normal series truncation approximation for computing the Weibull renewal function publication-title: Reliability Engineering and System Safety doi: 10.1016/j.ress.2007.03.026 – volume: 46 start-page: 1352 issue: 11 year: 1995 end-page: 1364 ident: CR5 article-title: On computations of the mean and variance of the number of renewals: A unified approach publication-title: Journal of the Operational Research Society doi: 10.1057/jors.1995.183 – year: 2008 ident: CR18 publication-title: Maintenance: Decision models for management – volume: 27 start-page: 348 issue: 3 year: 1995 end-page: 357 ident: CR23 article-title: Algorithms for the free replacement warranty with phase-type Iifetime distributions publication-title: IIE Transactions doi: 10.1080/07408179508936750 – volume: 40 start-page: 324 issue: 3 year: 2008 end-page: 340 ident: CR4 article-title: A stochastic model for joint inventory and outbound shipment decisions publication-title: IIE Transactions doi: 10.1080/07408170701487989 – start-page: 225 year: 2011 end-page: 269 ident: CR13 article-title: Efficient product support—Optimum and realistic spare parts forecasting publication-title: Replacement models with minimal repair doi: 10.1007/978-0-85729-215-5_9 – volume: 56 start-page: 33 year: 2015 end-page: 40 ident: CR25 article-title: Analytic and computational analysis of the discrete-time GI/D-MSP/1 queue using roots publication-title: Computers & Operations Research doi: 10.1016/j.cor.2014.10.017 – volume: 38 start-page: 88 issue: 38 year: 2014 end-page: 101 ident: CR24 article-title: Reliability analysis of shock-based deterioration using phase-type distributions publication-title: Probabilistic Engineering Mechanics doi: 10.1016/j.probengmech.2014.09.004 – year: 2003 ident: CR2 publication-title: Case studies in reliability and maintenance – volume: 32 start-page: 1 issue: 1 year: 2003 end-page: 16 ident: CR7 article-title: Some normal approximations for renewal function of large Weibull shape parameter publication-title: Communications in Statistics-Simulation and Computation doi: 10.1081/SAC-120013107 – ident: CR9 – volume: 146 start-page: 142 issue: 1 year: 2013 end-page: 152 ident: CR22 article-title: An improved approximation for the renewal function and its integral with an application in two-echelon inventory management publication-title: International Journal of Production Economics doi: 10.1016/j.ijpe.2013.06.016 – volume: 18 start-page: 281 issue: 1 year: 1989 end-page: 293 ident: CR28 article-title: On the solution of renewal-type integral equations publication-title: Communications in Statistics-Simulation and Computation doi: 10.1080/03610918908812760 – volume: 24 start-page: 9 issue: 1 year: 1997 end-page: 27 ident: CR6 article-title: Weibull renewal function for moderate to large arguments publication-title: Computational Statistics & Data Analysis doi: 10.1016/S0167-9473(96)00052-7 – start-page: 283 year: 2015 end-page: 301 ident: CR16 article-title: Product warranty publication-title: Introduction to quality and reliability engineering doi: 10.1007/978-3-662-47215-6_16 – volume: 29 start-page: 73 issue: 1 year: 1989 end-page: 80 ident: CR27 article-title: A simple approximation for IFR Weibull renewal functions publication-title: Microelectronics Reliability doi: 10.1016/0026-2714(89)90012-7 – volume: 12 start-page: 465 issue: 4 year: 2016 end-page: 480 ident: CR3 article-title: Stochastic approach to planning of spares for complex deteriorating industrial system publication-title: Quality Technology and Quantitative Management doi: 10.1080/16843703.2015.11673431 – volume: 12 start-page: 465 issue: 4 year: 2016 ident: 3356_CR3 publication-title: Quality Technology and Quantitative Management doi: 10.1080/16843703.2015.11673431 – volume: 12 start-page: 555 issue: 4 year: 2010 ident: 3356_CR29 publication-title: Methodology and Computing in Applied Probability doi: 10.1007/s11009-008-9098-y – volume-title: Case studies in reliability and maintenance year: 2003 ident: 3356_CR2 – volume: 48 start-page: 82 issue: 2 year: 1999 ident: 3356_CR1 publication-title: IEEE Transactions on Reliability doi: 10.1109/24.784278 – volume: 32 start-page: 1 issue: 1 year: 2003 ident: 3356_CR7 publication-title: Communications in Statistics-Simulation and Computation doi: 10.1081/SAC-120013107 – volume: 93 start-page: 616 issue: 4 year: 2008 ident: 3356_CR14 publication-title: Reliability Engineering and System Safety doi: 10.1016/j.ress.2007.03.026 – volume: 180 start-page: 302 year: 2018 ident: 3356_CR17 publication-title: Reliability Engineering and System Safety doi: 10.1016/j.ress.2018.07.030 – volume-title: Maintenance: Decision models for management year: 2008 ident: 3356_CR18 – volume: 56 start-page: 33 year: 2015 ident: 3356_CR25 publication-title: Computers & Operations Research doi: 10.1016/j.cor.2014.10.017 – volume: 70 start-page: 265 issue: 2 year: 1997 ident: 3356_CR8 publication-title: Stochastic Processes and their Applications doi: 10.1016/S0304-4149(97)00045-8 – volume: 30 start-page: 113 issue: 1 year: 2001 ident: 3356_CR10 publication-title: Communications in Statistics-Simulation and Computation doi: 10.1081/SAC-100001862 – start-page: 225 volume-title: Replacement models with minimal repair year: 2011 ident: 3356_CR13 doi: 10.1007/978-0-85729-215-5_9 – volume: 18 start-page: 281 issue: 1 year: 1989 ident: 3356_CR28 publication-title: Communications in Statistics-Simulation and Computation doi: 10.1080/03610918908812760 – volume: 47 start-page: 66 issue: 1 year: 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Engineering Mechanics doi: 10.1016/j.probengmech.2014.09.004 – volume: 33 start-page: 639 issue: 3 year: 2004 ident: 3356_CR12 publication-title: Communications in Statistics. Theory and Methods doi: 10.1081/STA-120028689 – volume: 40 start-page: 324 issue: 3 year: 2008 ident: 3356_CR4 publication-title: IIE Transactions doi: 10.1080/07408170701487989 – volume: 46 start-page: 1352 issue: 11 year: 1995 ident: 3356_CR5 publication-title: Journal of the Operational Research Society doi: 10.1057/jors.1995.183 – volume: 27 start-page: 348 issue: 3 year: 1995 ident: 3356_CR23 publication-title: IIE Transactions doi: 10.1080/07408179508936750 – volume: 24 start-page: 9 issue: 1 year: 1997 ident: 3356_CR6 publication-title: Computational Statistics & Data Analysis doi: 10.1016/S0167-9473(96)00052-7 – volume: 95 start-page: 963 issue: 9 year: 2010 ident: 3356_CR15 publication-title: Reliability Engineering and System Safety doi: 10.1016/j.ress.2010.04.007 – volume: 146 start-page: 142 issue: 1 year: 2013 ident: 3356_CR22 publication-title: International Journal of Production Economics doi: 10.1016/j.ijpe.2013.06.016 – volume: 29 start-page: 73 issue: 1 year: 1989 ident: 3356_CR27 publication-title: Microelectronics Reliability doi: 10.1016/0026-2714(89)90012-7 |
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| SubjectTerms | Accuracy Approximation Approximation theory Business and Management Combinatorics Distribution functions Inventory control Mathematical optimization Methods Operations research Operations Research/Decision Theory Optimization Reliability (Engineering) S.I. : Reliability Modeling with Applications Based on Big Data Theory of Computation |
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| Title | Two approximations of renewal function for any arbitrary lifetime distribution |
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