三种损失函数下系统可靠度的Bayes算法——以串并联系统为例
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摘要
损失函数是一种衡量损失和错误程度的函数,将损失函数与Bayes统计相结合,构建出系统可靠度及后验分布参数的三种损失函数的算法。文中选取双边截尾的样本,当参数的先验分布服从伽玛分布时,以串并联系统为例,推导三种损失函数下的系统可靠度及后验分布参数的Bayes算法。并采用Monte-Carlo实验法随机产生多组数值取均值后,计算出该三种损失函数可靠性的估计值。
Making use of the loss function is a property of measuring loss degree and error degree. The loss function is combined with Bayes statistics, which constructs three kinds of loss functions algorithm about system reliability and posterior distribution parameters. In this paper, we select bilateral truncated samples. when the prior distribution of the parameters obeys gamma distribution, and we take series-parallel system as an example to derive system reliability degree and the posterior distribution parameter of the Bayes algorithm under three kinds of loss function. Moreover, adopting Monte Carlo experiment method to generate the mean of multiple sets of values at random, the estimate of the reliability of the three kinds of loss functions is calculated.
Making use of the loss function is a property of measuring loss degree and error degree. The loss function is combined with Bayes statistics, which constructs three kinds of loss functions algorithm about system reliability and posterior distribution parameters. In this paper, we select bilateral truncated samples. when the prior distribution of the parameters obeys gamma distribution, and we take series-parallel system as an example to derive system reliability degree and the posterior distribution parameter of the Bayes algorithm under three kinds of loss function. Moreover, adopting Monte Carlo experiment method to generate the mean of multiple sets of values at random, the estimate of the reliability of the three kinds of loss functions is calculated.
引文
[1]李凌,师义民,李明海.逐步增加的II型截尾下冷贮备串联系统可靠性指标的Bayes估计[J].工程数学学报,2007,24(5):895-901.
[2]冯艳,师义民,严惠元.定数截尾两参数指数——威布尔分布形状参数的Bayes估计[J].数学的实践与认识,2007,37(5):37-45.
[3]师义民.双边截断型分布族参数的经验Bayes估计[J].高校应用数学学报A辑,2000.15A(4):475-483.
[4]李秀春,师义民,魏杰琼.冷贮备串联系统可靠性指标的经验Bayes近似置信限[J].系统工程,2005,23(3):101-104.
[5]康达.并串联系统可靠度的Bayes估计及Bayes置信限[J].温州大学学报,2010,31(3):17-23.
[2]冯艳,师义民,严惠元.定数截尾两参数指数——威布尔分布形状参数的Bayes估计[J].数学的实践与认识,2007,37(5):37-45.
[3]师义民.双边截断型分布族参数的经验Bayes估计[J].高校应用数学学报A辑,2000.15A(4):475-483.
[4]李秀春,师义民,魏杰琼.冷贮备串联系统可靠性指标的经验Bayes近似置信限[J].系统工程,2005,23(3):101-104.
[5]康达.并串联系统可靠度的Bayes估计及Bayes置信限[J].温州大学学报,2010,31(3):17-23.