中文

Operations Research Transactions >

2025 , Vol. 29 >Issue 4: 191 - 204

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2025.04.015

Research Article

Research on the waiting time distribution of a machine maintenance model with replaceable repair facility and repairman's multiple vacations

  • Wenqing WU ,
  • Haiwen XU ,
  • Miaomiao YU ,
  • Kelong ZHENG
Expand
  • 1. Faculty of Science, Civil Aviation Flight University of China, Chengdu 641419, Sichuan, China
    2. School of Mathematical Sciences, Sichuan Normal University, Chengdu 610068, Sichuan, China

Received date: 2022-11-16

  Online published: 2025-12-11

Copyright

, 2025, All rights reserved. Unauthorized reproduction is prohibited.
Fold

Abstract

This paper considers the waiting time distribution of an arbitrary failed machine in a machine repair system with a replaceable repair facility and repairman's multiple vacations where the operating time and the repair time of machines all follow exponential distributions. By employing the Markov Chain with absorbing time, the probabilistic properties of the phase-type distribution and the Laplace-Stieltjes transform, the specific expressions of the waiting time distribution of failed machines and its mean waiting time are all derived. Based on this, we discuss the time-dependent behavior of the system performance measures and provide numerical results of the waiting time.

Key words： machine repair system; replaceable repair facility; multiple vacations; phase type distribution; the waiting time distribution of failed machine

Cite this article

Wenqing WU , Haiwen XU , Miaomiao YU , Kelong ZHENG . Research on the waiting time distribution of a machine maintenance model with replaceable repair facility and repairman's multiple vacations[J]. Operations Research Transactions, 2025 , 29(4) : 191 -204 . DOI: 10.15960/j.cnki.issn.1007-6093.2025.04.015

References

1 Palm C . The distribution of repairmen in serving automatic machines[J]. Industritidningen Norden, 1947, 75, 75- 80.
2 Gross D , Shortle J F , Thompson J M , et al. Fundamentals of Queueing Theory[M]. New York: Wiley & Sons, 2008.
3 高春燕. 兼职辅助业务的机器维修模型[D]. 秦皇岛: 燕山大学, 2006.
4 孟艳丽. 基于有限源排队的机器维修模型的优化研究[D]. 大连: 大连海事大学, 2019.
5 付永红, 余玅妙, 唐应辉, 等. 两水平修理策略下的M/(Mr, Gs)/1/N/N机器维修模型稳态概率算法与性能分析[J]. 山东大学学报(理学版), 2009, 4 (44): 72- 78.
6 张静. 带有休假策略的温贮备机器维修问题的性能分析[D]. 秦皇岛: 燕山大学, 2012.
7 Ke J C , Wang K H . Vacation policies for machine repair problem with two type spares[J]. Applied Mathematical Modelling, 2007, 31 (5): 880- 894.
8 Wang K H , Chen W L , Yang D Y . Optimal management of the machine repair problem with working vacation: Newton's method[J]. Journal of Computational and Applied Mathematics, 2009, 233 (2): 449- 458.
9 Ke J C , Wu C H . Multi-server machine repair model with standbys and synchronous multiple vacation[J]. Computers & Industrial Engineering, 2012, 62 (1): 296- 305.
10 Wang K H , Su J H , Yang D Y . Analysis and optimization of an M/G/1 machine repair problem with multiple imperfect coverage[J]. Applied Mathematics and Computation, 2014, 242 (1): 590- 600.
11 Chen W L , Wang K H . Reliability analysis of a retrial machine repair problem with warm standbys and a single server with N-policy[J]. Reliability Engineering & System Safety, 2018, 180 (12): 476- 486.
12 曹晋华. 服务设备可修的机器服务模型分析[J]. 数学研究与评论, 1985, 5 (4): 89- 96.
13 Tang Y H . Revisiting the model of servicing machines with repairable service facility-a new analyzing idea and some new results[J]. Acta Mathematicae Sinica, 2010, 26 (4): 557- 566.
14 Neuts M F . Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach[M]. Baltimore: The Johns Hopkins University Press, 1981.
Options
Outlines

/

〈 〉