Robust estimation of dependent competing risk model under interval monitoring and determining optimal inspection intervals
Recently, a growing interest is evident in modelling dependent competing risks in lifetime prognosis problems. In this work, we propose to model the dependent competing risks by Marshal‐Olkin bivariate exponential distribution. The observable data consists of a number of failures due to different ca...
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| Veröffentlicht in: | Applied stochastic models in business and industry Jg. 40; H. 4; S. 926 - 944 |
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01.07.2024
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| Abstract | Recently, a growing interest is evident in modelling dependent competing risks in lifetime prognosis problems. In this work, we propose to model the dependent competing risks by Marshal‐Olkin bivariate exponential distribution. The observable data consists of a number of failures due to different causes across different time intervals. The failure count data is common in instances like one‐shot devices where the state of the subjects is inspected at different inspection times rather than the exact failure times. The point estimation of the lifetime distribution in the presence of competing risk has been studied through a divergence‐based robust estimation method called minimum density power divergence estimation (MDPDE) with and without constraint. The optimal value of the tuning parameter has been obtained. The testing of the hypothesis is performed based on a Wald‐type test statistic. The influence function is derived for the point estimator and the test statistic, reflecting the degree of robustness. Another key contribution of this work is determining the optimal inspection times based on predefined objectives. This article presents the determination of multi‐criteria‐based optimal design. Population‐based heuristic algorithm nondominated sorting‐based multiobjective Genetic algorithm is exploited to solve this optimization problem. |
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| AbstractList | Recently, a growing interest is evident in modelling dependent competing risks in lifetime prognosis problems. In this work, we propose to model the dependent competing risks by Marshal‐Olkin bivariate exponential distribution. The observable data consists of a number of failures due to different causes across different time intervals. The failure count data is common in instances like one‐shot devices where the state of the subjects is inspected at different inspection times rather than the exact failure times. The point estimation of the lifetime distribution in the presence of competing risk has been studied through a divergence‐based robust estimation method called minimum density power divergence estimation (MDPDE) with and without constraint. The optimal value of the tuning parameter has been obtained. The testing of the hypothesis is performed based on a Wald‐type test statistic. The influence function is derived for the point estimator and the test statistic, reflecting the degree of robustness. Another key contribution of this work is determining the optimal inspection times based on predefined objectives. This article presents the determination of multi‐criteria‐based optimal design. Population‐based heuristic algorithm nondominated sorting‐based multiobjective Genetic algorithm is exploited to solve this optimization problem. |
| Author | Mondal, Shuvashree Baghel, Shanya |
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| Cites_doi | 10.1080/01621459.1967.10482885 10.1007/s00184‐019‐00718‐5 10.1002/asmb.693 10.1017/S0269964818000049 10.1080/08982112.2017.1390585 10.1016/j.ress.2014.12.014 10.1080/03610926.2017.1397170 10.1214/17-EJS1295 10.1080/02664763.2020.1736524 10.1080/03610926.2015.1129420 10.1080/02664763.2015.1016901 10.1016/j.apm.2023.10.037 10.1002/asmb.457 10.1007/s13571-017-0143-0 10.1016/j.csda.2011.09.010 10.1201/9781420035902 10.1214/13‐EJS847 10.1016/j.cam.2020.113214 10.1080/00949650412331299120 10.1080/01966324.1987.10737213 10.1002/asmb.465 10.1016/j.ress.2014.01.009 10.1109/TIT.2019.2903244 10.1007/978-3-031-15509-3_4 10.1016/j.jspi.2008.05.030 10.1002/asmb.2242 10.1198/004017004000000482 10.1002/asmb.2671 10.1093/biomet/85.3.549 10.1016/j.csda.2014.08.002 10.1007/s13571‐022‐00289‐y 10.1161/CIRCULATIONAHA.115.017719 10.1109/4235.996017 |
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| SubjectTerms | Bivariate analysis competing risk Design optimization divergence based robust estimation Failure times Genetic algorithms Heuristic methods influence function Influence functions Inspection Intervals Marshal‐Olkin bivariate exponential distribution Multiple objective analysis multi‐objective optimization Probability distribution functions Robustness Service life assessment Sorting algorithms |
| Title | Robust estimation of dependent competing risk model under interval monitoring and determining optimal inspection intervals |
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