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1. 北京航空航天大学可靠性与系统工程学院, 北京 100083;
2. 南京理工大学理学院, 南京 210094;
3. 军械工程学院装备指挥与管理系, 石家庄 050003

Theory analysis of system instantaneous availability under uniform distribution
YANG Yi1 , REN Sichao2, YU Yongli3
1. School of Reliability and Systems Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;
2. School of Sciences, Nanjing University of Science and Technology, Nanjing 210094, China;
3. Department of Equipment Command and Management, Ordnance Engineering College, Shijiazhuang 050003, China
Received: 2015-01-29; Accepted: 2015-04-17; Published online: 2015-05-22
Foundation items: National Natural Science Foundation of China (61104132, 61573041)
Abstract:The early volatility of instantaneous availability which belonged to one-unit repairable system was analyzed in theory. Recent research progress on two kinds of availabilities was reported and the importance of research on the instantaneous availability was highlighted. It was respectively discussed that the failure time and repair time of system components obeyed the same as well as different uniform distribution, and then the renewal equation was transformed into piecewise ordinary differential equations or delay differential equations. The analytical expressions of instantaneous availability were obtained from the differential equations by the use of the continuity and initial value. A method was put forward to judge the volatility of instantaneous availability, that is, to judge whether there existed the value of instantaneous availability less than that of the steady-state availability. The method has been proved to be effective, and the conclusion demonstrates that the volatility exists regardless of any parameter combination under uniform distribution. The final simulation results are in good agreement with the theoretical results.
Key words: instantaneous availability     steady-state availability     uniform distribution     volatility     differential equation

1.2 模型引入

 图 1 X和Y服从相同均匀分布时瞬时可用度对比曲线Fig. 1 Comparative curves of instantaneous availability when X and Y obey the same uniform distributions

Q(t)代入更新方程(1),得到如下的瞬时可用度的积分方程：

 图 2 函数f(t)的图像Fig. 2 Image of function f(t)

 图 3 X和Y服从不同均匀分布瞬时可用度比较曲线Fig. 3 Comparative curves of instantaneous availability when X and Y obey different uniform distributions
3 结 论

1) 当故障时间X和修复时间Y服从相同的均匀分布时,瞬时可用度在第1个分段函数中存在小于稳态可用度的点,所以由可用度的稳定性可以说明A(t)至少存在一次波动。

2) 当故障时间X和修复时间Y服从不同的均匀分布时,瞬时可用度在第1个分段函数中也存在小于稳态可用度的点,所以说明A(t)至少存在一次波动。

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文章信息

YANG Yi, REN Sichao, YU Yongli

Theory analysis of system instantaneous availability under uniform distribution

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(1): 28-34.
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0058