# [1]王冠军,张元林.维修时间受限的单部件系统几何过程维修模型[J].东南大学学报(自然科学版),2013,43(6):1335-1339.[doi:10.3969/j.issn.1001-0505.2013.06.037] 　Wang Guanjun,Zhang Yuanlin.Geometric process model for a single-unit system with limit repair time[J].Journal of Southeast University (Natural Science Edition),2013,43(6):1335-1339.[doi:10.3969/j.issn.1001-0505.2013.06.037] 点击复制 维修时间受限的单部件系统几何过程维修模型() 分享到： var jiathis_config = { data_track_clickback: true };

43

2013年第6期

1335-1339

2013-11-20

## 文章信息/Info

Title:
Geometric process model for a single-unit system with limit repair time

Author(s):
Department of Mathematics, Southeast University, Nanjing 210096, China

Keywords:

O212.2
DOI:
10.3969/j.issn.1001-0505.2013.06.037

Abstract:
By applying the geometric process repair theory, the optimal repair replacement policy for a single-unit system with limit repair time is studied. Assume that the operating times of the system after repair decrease stochastically forming a geometric process, while the consecutive repair times constitute an increasing geometric process. An upper threshold θ is set for the repair time. If the repair is not completed in the given limit repair time θ, the repair is stopped and the system is replaced by a new one. If the system is repaired N times, the system will be replaced at the next failure. Assume that the working time follows a general distribution, and the repair time is exponentially distributed. Through some analysis, some reliability indices for the system including the average availability and the average occurrence of failure are obtained. The explicit expression for the long-run average cost rate is also obtained. A numerical example is given to simulate the optimal replacement policy N*, and the influence of the limit repair time on the optimal replacement policy is also discussed.

## 参考文献/References:

[1] Lam Y. Geometric processes and replacement problem [J]. Acta Mathematica Applicandae Sinica, 1988, 4(4): 366-377.
[2] Lam Y. A note on the optimal replacement problem [J]. Advances in Applied Probability, 1988, 20(2): 479-482.
[3] Zhang Yuanlin. A bivariate optimal replacement policy for a repairable system [J]. Journal of Applied Probability, 1994, 31(4):1123-1127.
[4] 王冠军,张元林.δ_冲击模型及其最优更换策略[J]. 东南大学学报:自然科学版,2001,31(5):121-124.
Wang Guanjun, Zhang Yuanlin.δ_shock model and the optimal replacement policy [J]. Journal of Southeast University: Natural Science Edition, 2001,31(5):121-124.(in Chinese)
[5] 王冠军,张元林. 一般δ_冲击模型及其最优更换策略[J]. 运筹学学报, 2003, 7(3):75-82.
Wang Guanjun, Zhang Yuanlin. General δ_shock model and its optimal replacement policy [J].OR Transactions,2003, 7(3):75-82.(in Chinese)
[6] Wang Guanjun, Zhang Yuanlin. A bivariate optimal replacement policy for a cold standby repairable system with preventive repair [J]. Applied Mathematics and Computation, 2011, 218(7):3158-3165.
[7] Zhang Yuanlin, Wang Guanjun. An extended replacement policy for a deteriorating system with multi-failure modes [J]. Applied Mathematics and Computation, 2011, 218(5): 1820-1830.
[8] Wang Guanjun, Zhang Yuanlin. Optimal repair-replacement policies for a system with two types of failures [J]. European Journal of Operational Research, 2013, 226(3): 500-506.
[9] Lam Y. The geometric process and its applications [M]. Singapore: World Scientific, 2007: 37-40.
[10] Nakagawa T, Osaki S. The optimum repair limit replacement policies [J]. Operational Research Quarterly, 1974, 25(2): 311-317.
[11] Wang H. A survey of maintenance policies of deteriorating systems [J]. European Journal of Operational Research, 2002, 139(3):249-489.
[12] Dohi T, Ashioka A. Replacement policy with imperfect repair: Lorenz transform approach [J]. Mathematical and Computer Modelling, 2003, 38(11): 1169-1176.
[13] Ross S M. Stochastic processes [M]. New York: Wiley, 1996:132-140.

## 相似文献/References:

[1]王冠军,张元林.δ-冲击模型及其最优更换策略[J].东南大学学报(自然科学版),2001,31(5):121.[doi:10.3969/j.issn.1001-0505.2001.05.026]
Wang Guanjun,Zhang Yuanlin.δ-Shock Model and the Optimal Replacement Policy[J].Journal of Southeast University (Natural Science Edition),2001,31(6):121.[doi:10.3969/j.issn.1001-0505.2001.05.026]