﻿ 成败型系统可靠性增长的Bayes评估
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Bayesian evaluation method for binomial system reliability growth
Yuan Kun, Li Xiaogang
School of Reliability and System Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
Abstract:Concerning the multi-stages field information during the process of product development, a Bayes evaluation method based on the new Dirichlet prior distribution was proposed. This method made use of discrete army material system analysis activity (AMSAA) model to describe the dynamic change of reliability at different stage and predicted the reliability at next stage according to the multi-stages field data during the reliability growth test (GRT). Then the new Dirichlet prior distribution was introduced and the parameter estimations were obtained by maximum entropy method. Under the conditions of gaining the field test data, the Bayesian evaluation of product reliability was obtained by the proposed method. Finally, numerical example demonstrates the accuracy of the proposed method with appropriate expert experience compared to the discrete AMSAA model and Beta prior distribution.
Key words: reliability growth     Bayesian estimation     new Dirichlet prior distribution     discrete AMSAA model     maximum entropy method

1 可靠性增长模型

Bayes方法评估产品可靠性重要在于先验分布的确定和参数的估计.文献[7]中采用次序Dirichlet作为先验分布,能较好地描述专家信息,但只用一个参数描述所有阶段的方差却并不合适.因此,Li等人[9]从一般的Beta分布出发,提出用条件分布的形式描述可靠性增长.在第k阶段未试验前,构造(Rk－1,1)上的截尾Beta分布作为该检测区间内产品可靠度的分布,称为新Dirichlet分布,即有

2 新Dirichlet先验分布的参数确定

3 离散AMSAA模型

4 可靠性Bayes估计

5 实例分析

 c 估计值 a b 后验 0.9 0.853 1.450 0.9380 0.8 1.140 0.912 0.9458 0.7 1.372 0.864 0.9390 0.6 1.688 0.844 0.9031 0.5 2.530 1.001 0.9203 0.4 2.550 0.850 0.9219 0.3 2.950 0.850 0.9172 0.2 3.350 0.850 0.9129 0.1 3.750 0.850 0.9091 0 4.140 0.850 0.9056

 4先验估计值 估计值 c a b 4后验 0.85 0.9 1.040 0.966 0.9566 0.85 0.6 2.414 0.848 0.9416 0.85 0.3 4.121 0.883 0.9272 0.90 0.9 1.448 0.852 0.9635 0.90 0.6 3.480 0.870 0.9479 0.90 0.3 5.889 0.906 0.9371 0.94 0.9 3.010 0.860 0.9705 0.94 0.6 6.710 0.915 0.9606 0.94 0.3 10.822 0.941 0.9552

6 结 论

1) 针对成败型系统的可靠性增长问题,在结合离散AMSAA模型的基础上,提出了基于新Dirichlet先验分布的评估模型.该模型能够充分利用各阶段的可靠性信息,在合适的专家经验指导下,能够较为准确地得到系统增长后的可靠性.

2) 该模型评估系统增长后的可靠性的精度与专家经验有关,在对当前阶段的可靠度无法给出恰当的估计时,该模型可以退化成Beta分布,具有一定的灵活性.

3) 相较于传统模型中采用的积分模型,该模型的计算过程较为简便,避免复杂的积分问题,能够保证计算结果的准确性.

1) 当离散AMSAA模型对上一阶段可靠性的估计存在明显偏差时,利用校正系数进行校正时,该系数选取值的大小存在主观性.如何给出校正系数客观公正的选取规则,是需要研究的问题.

2) 上一阶段可靠性估计不准确也可能会导致利用最大熵模型得不到先验分布的参数,此时同样需要借助校正系数进行改进.在选取校正系数时,也需要同时考虑极大熵模型的影响.

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#### 文章信息

Yuan Kun, Li Xiaogang

Bayesian evaluation method for binomial system reliability growth

Journal of Beijing University of Aeronautics and Astronsutics, 2014, 40(9): 1312-1316.
http://dx.doi.org/10.13700/j.bh.1001-5965.2013.0599