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Dynamical distribution of continuous service time model involving non-Maxwellian collision kernel and value functions

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Chinese Physics B 2024年第9期33卷 340-348页

作者： Minfang Zhao Lingting Kong Miao Liu Shaoyong Lai School of Mathematics and Statistics Yili Normal UniversityYining 835000China Institute of Applied Mathematics Yili Normal UniversityYining 835000China School of Mathematics Southwestern University of Finance and EconomicsChengdu 611130China

The distribution of continuous service time in call centers is investigated.A non-Maxwellian collision kernel combining two different value functions in the interaction rule are used to describe the evolution of continuous service time,*** the statistical mechanical and asymptotic limit methods,Fokker–Planck equations are derived from the corresponding Boltzmann-type equations with non-Maxwellian collision *** steady-state solutions of the Fokker–Planck equation are obtained in exact *** experiments are provided to support our results under different parameters.

关键词： kinetic theory service time Fokker-Planck equation value function

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Correlation analysis between fault frequency and service time of underground fluid instruments

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Geodesy and Geodynamics 2023年第4期14卷 411-418页

作者： Xiao Tian Guoying Su The First Monitoring and Application Center China Earthquake AdministrationTianjin 300180China

In this paper, we make a statistical analysis of the fault information of the underground fluid instruments of 12 models in China from January 2021 to May 2022 based on the Pearson correlation coefficient, and compare the fault statistics of the meteorological three-element instruments of 3 models during the study period. The results show that:(1) The numbers of faults of the underground fluid instruments of 12models with different service times are basically positively correlated with the numbers of the corresponding instruments, with good consistency. Moreover, the automatic observation instruments(8models) with more than 30 units are significantly correlated at a 0.05 significance level(95% confidence level). Even at a 0.01 significance level(99% confidence level), there are 7 models(7/8) with significant correlation.(2) The positive and negative correlations between the monthly average number of faults and the corresponding service times of the underground fluid instruments of 12 models with different service times are random, and there are 9 models(75%) with no significant correlation at a 0.05 significance level(95% confidence level), while 12 models(100%) with no significant correlation at a 0.01significance level(99% confidence level).(3) The monthly average numbers of faults of the underground fluid instruments of 12 models are basically 0.02-0.05 times/(unit·month), and the overall fault frequency is low.(4) The fault statistics results of the meteorological three-element instruments of 3 models are consistent with the characteristics of the underground fluid instruments of 12 models. In general,there is no significant correlation between the fault frequency and the service time of underground fluid instruments.(5) The results of this paper demonstrate that the service time of underground fluid instruments cannot be taken as the main reason for whether to update the instruments. Similarly, the fault frequency of the instruments cannot be taken as the main

关键词： Underground fluid instruments Fault frequency service time Correlation analysis

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ON THE COMPLETION time OF A JOB PROCESSED ON AN UNRELIABLE MACHINE

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Acta Mathematicae Applicatae Sinica 2001年第3期17卷 418-425页

作者：岳德权涂菶生 Department of Mathematics Yanshan University Qinhuangdao China Department of Automation Nankai University Tianjin China

In this paper, we consider the completion time of a job processed on an unreliable machine. Assume that the lifetime and the repair time of the machine and the service time of the job have general distributions. We obtain the Laplace-Stieltjes transforms and the expectations of the distributions of the completion time, the interruption time and the actual service time. Under some special cases, we derive sufficient and necessary (or sufficient) conditions such that the completion time is larger and smaller than the service time in the sense of the Laplace transform order (or the expectation), respectively

关键词： Completion time interruption time service time unreliable machine Laplace transform order

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