Two novel critical shock models based on Markov renewal processes
In this paper, we investigate systems subject to random shocks that are classified into critical and noncritical categories, and develop two novel critical shock models. Classical extreme shock models and run shock models are special cases of our developed models. The system fails when the total num...
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| Published in | Naval research logistics Vol. 69; no. 1; pp. 163 - 176 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Hoboken, USA
John Wiley & Sons, Inc
01.02.2022
Wiley Subscription Services, Inc |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0894-069X 1520-6750 |
| DOI | 10.1002/nav.21991 |
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| Abstract | In this paper, we investigate systems subject to random shocks that are classified into critical and noncritical categories, and develop two novel critical shock models. Classical extreme shock models and run shock models are special cases of our developed models. The system fails when the total number of critical shocks reaches a predetermined threshold, or when the system stays in an environment that induces critical shocks for a preset threshold time, corresponding to failure mechanisms of the developed two critical shock models respectively. Markov renewal processes are employed to capture the magnitude and interarrival time dependency of environment‐induced shocks. Explicit formulas for systems under the two critical shock models are derived, including the reliability function, the mean time to failure and so on. Furthermore, the two critical shock models are extended to the random threshold case and the integrated case where formulas of the reliability indexes of the systems are provided. Finally, a case study of a lithium‐ion battery system is conducted to illustrate the proposed models and the obtained results. |
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| AbstractList | In this paper, we investigate systems subject to random shocks that are classified into critical and noncritical categories, and develop two novel critical shock models. Classical extreme shock models and run shock models are special cases of our developed models. The system fails when the total number of critical shocks reaches a predetermined threshold, or when the system stays in an environment that induces critical shocks for a preset threshold time, corresponding to failure mechanisms of the developed two critical shock models respectively. Markov renewal processes are employed to capture the magnitude and interarrival time dependency of environment‐induced shocks. Explicit formulas for systems under the two critical shock models are derived, including the reliability function, the mean time to failure and so on. Furthermore, the two critical shock models are extended to the random threshold case and the integrated case where formulas of the reliability indexes of the systems are provided. Finally, a case study of a lithium‐ion battery system is conducted to illustrate the proposed models and the obtained results. |
| Author | Wu, Bei Qiu, Qingan Cui, Lirong |
| Author_xml | – sequence: 1 givenname: Bei orcidid: 0000-0003-2654-1203 surname: Wu fullname: Wu, Bei email: 315562327@qq.com organization: Northwestern Polytechnical University – sequence: 2 givenname: Lirong orcidid: 0000-0002-8987-4307 surname: Cui fullname: Cui, Lirong organization: Beijing Institute of Technology – sequence: 3 givenname: Qingan orcidid: 0000-0001-8741-0536 surname: Qiu fullname: Qiu, Qingan organization: Beijing Institute of Technology |
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| Cites_doi | 10.1016/j.spl.2006.08.008 10.1016/j.ress.2019.106513 10.1016/j.cam.2018.09.022 10.1016/j.ress.2018.01.006 10.1177/1748006X19864831 10.1109/TR.2007.895306 10.1016/j.ress.2016.10.006 10.1016/j.ress.2020.106827 10.1109/TR.2006.879661 10.1016/j.cam.2012.06.008 10.1002/(SICI)1520-6750(199604)43:3<319::AID-NAV1>3.0.CO;2-C 10.1214/aop/1176996891 10.1080/0740817X.2012.676749 10.1002/nav.21642 10.1016/j.ress.2019.106516 10.1002/nav.20068 10.1239/jap/1300198148 10.1016/j.ress.2019.03.045 10.1002/1520-6750(199104)38:2<145::AID-NAV3220380203>3.0.CO;2-D 10.1017/jpr.2018.83 10.1016/j.spl.2011.10.022 10.1016/j.ress.2020.107051 10.1239/jap/996986754 10.1016/j.cam.2018.12.011 10.1080/00207720500032606 10.2307/3215132 10.1023/A:1004113825283 10.1023/A:1009959004020 10.1016/j.spl.2005.04.043 10.2307/3213896 10.1007/978-1-4471-6395-4 10.1016/j.cie.2020.106509 10.1007/s10958-006-0306-4 |
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| References_xml | – volume: 234 start-page: 129 issue: 1 year: 2020 end-page: 137 article-title: Reliability assessment of system under a generalized cumulative shock model publication-title: Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability – volume: 45 start-page: 244 issue: 3 year: 2013 end-page: 258 article-title: Protecting critical infrastructures against intentional attacks: A two‐stage game with incomplete information publication-title: IIE Transactions – volume: 77 start-page: 577 issue: 6 year: 2007 end-page: 587 article-title: Life behavior of δ‐shock model publication-title: Statistics & Probability Letters – volume: 36 start-page: 209 issue: 4 year: 2005 end-page: 214 article-title: A shock model with two‐type failures and optimal replacement policy publication-title: International Journal of Systems Science – volume: 190 year: 2019 article-title: Reliability and optimal replacement policy for an extreme shock model with a change point publication-title: Reliability Engineering & System Safety – volume: 159 start-page: 1 year: 2017 end-page: 11 article-title: Reliability assessment of competing risks with generalized mixed shock models publication-title: Reliability Engineering & System Safety – volume: 56 start-page: 340 issue: 2 year: 2007 end-page: 348 article-title: Reliability analysis on the δ‐shock model of complex systems publication-title: IEEE Transactions on Reliability – volume: 20 start-page: 600 issue: 3 year: 1983 end-page: 614 article-title: General shock models associated with correlated renewal sequences publication-title: Journal of Applied Probability – volume: 38 start-page: 145 issue: 2 year: 1991 end-page: 156 article-title: A cumulative damage shock model with imperfect preventive maintenance publication-title: Naval Research Logistics – volume: 82 start-page: 326 issue: 2 year: 2012 end-page: 331 article-title: Generalized δ‐shock model via runs publication-title: Statistics & Probability Letters – volume: 52 start-page: 253 issue: 3 year: 2005 end-page: 260 article-title: Shock model in Markovian environment publication-title: Naval Research Logistics – volume: 197 start-page: 106827 year: 2020 article-title: Failure interaction model based on extreme shock and Markov processes publication-title: Reliability Engineering & System Safety – volume: 32 start-page: 821 issue: 3 year: 1995 end-page: 831 article-title: Analysis of Markov renewal shock models publication-title: Journal of Applied Probability – year: 2014 – volume: 48 start-page: 258 issue: 1 year: 2011 end-page: 270 article-title: On new classes of extreme shock models and some generalizations publication-title: Journal of Applied Probability – volume: 190 start-page: 106516 year: 2019 article-title: Reliability analysis of semi‐Markov systems with restriction on transition times publication-title: Reliability Engineering & System Safety – volume: 2 start-page: 295 year: 1999 end-page: 307 article-title: Extreme shock models publication-title: Extremes – volume: 55 start-page: 542 issue: 3 year: 2006 end-page: 550 article-title: Generalized shock models based on a cluster point process publication-title: IEEE Transactions on Reliability – volume: 1 start-page: 627 issue: 4 year: 1973 end-page: 649 article-title: Shock models and wear processes publication-title: The Annals of Probability – volume: 349 start-page: 52 year: 2019 end-page: 59 article-title: Reliability analysis under Marshall–Olkin run shock model publication-title: Journal of Computational and Applied Mathematics – volume: 192 start-page: 106047 year: 2019 article-title: A new cumulative shock model with damage and inter‐arrival time dependency publication-title: Reliability Engineering & System Safety – volume: 188 start-page: 393 year: 2019 end-page: 397 article-title: Reliability and optimal replacement policy for a ‐out‐of‐ system subject to shocks publication-title: Reliability Engineering & System Safety – volume: 62 start-page: 483 issue: 6 year: 2015 end-page: 492 article-title: Life distribution analysis based on Lévy subordinators for degradation with random jumps publication-title: Naval Research Logistics – volume: 138 start-page: 5410 year: 2006 end-page: 5414 article-title: Asymptotic results for a run and cumulative mixed shock model publication-title: Journal of Mathematical Sciences – volume: 31 start-page: 99 year: 2001 end-page: 104 article-title: Electrical characteristics of 18650 Li‐ion cells at low temperatures publication-title: Journal of Applied Electrochemistry – volume: 38 start-page: 438 issue: 2 year: 2001 end-page: 448 article-title: Shocks, runs and random sums publication-title: Journal of Applied Probability – volume: 237 start-page: 384 issue: 1 year: 2013 end-page: 388 article-title: On the lifetime behavior of a discrete time shock model publication-title: Journal of Computational and Applied Mathematics – volume: 145 start-page: 106509 year: 2020b article-title: Reliability of multi‐state systems under Markov renewal shock models with multiple failure levels publication-title: Computers & Industrial Engineering – volume: 55 start-page: 1249 issue: 4 year: 2018 end-page: 1260 article-title: Reliability assessment of system under a generalized run shock model publication-title: Journal of Applied Probability – volume: 202 start-page: 107051 year: 2020a article-title: Reliability evaluation of Markov renewal shock models with multiple failure mechanisms publication-title: Reliability Engineering & System Safety – volume: 43 start-page: 319 issue: 3 year: 1996 end-page: 333 article-title: Optimal number of minimal repairs before replacement of a system subject to shocks publication-title: Naval Research Logistics – volume: 74 start-page: 187 issue: 2 year: 2005 end-page: 204 article-title: Realistic variation of shock models publication-title: Statistics & Probability Letters – volume: 352 start-page: 255 year: 2019 end-page: 261 article-title: Reliability evaluation of a system under a mixed shock model publication-title: Journal of Computational and Applied Mathematics – ident: e_1_2_9_18_1 doi: 10.1016/j.spl.2006.08.008 – ident: e_1_2_9_8_1 doi: 10.1016/j.ress.2019.106513 – ident: e_1_2_9_24_1 doi: 10.1016/j.cam.2018.09.022 – ident: e_1_2_9_26_1 doi: 10.1016/j.ress.2018.01.006 – ident: e_1_2_9_11_1 doi: 10.1177/1748006X19864831 – ident: e_1_2_9_19_1 doi: 10.1109/TR.2007.895306 – ident: e_1_2_9_25_1 doi: 10.1016/j.ress.2016.10.006 – ident: e_1_2_9_22_1 doi: 10.1016/j.ress.2020.106827 – ident: e_1_2_9_2_1 doi: 10.1109/TR.2006.879661 – ident: e_1_2_9_6_1 doi: 10.1016/j.cam.2012.06.008 – ident: e_1_2_9_29_1 doi: 10.1002/(SICI)1520-6750(199604)43:3<319::AID-NAV1>3.0.CO;2-C – ident: e_1_2_9_10_1 doi: 10.1214/aop/1176996891 – ident: e_1_2_9_35_1 doi: 10.1080/0740817X.2012.676749 – volume-title: Introduction to probability models year: 2014 ident: e_1_2_9_27_1 – ident: e_1_2_9_30_1 doi: 10.1002/nav.21642 – ident: 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| SubjectTerms | Failure mechanisms Lithium Lithium-ion batteries Markov analysis Markov chain Markov renewal process Mean time to failure Reliability reliability function Renewal shock model Time dependence |
| Title | Two novel critical shock models based on Markov renewal processes |
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