基于混合威布尔分布的应力-强度模型可靠度估计

Reliability estimation of stress-strength model based on mixed Weibull distribution

为了获得产品完全的故障数据和相对准确的可靠度,在逐步Ⅰ型区间删失下,假设应力和强度变量相互独立,应力变量服从一个Lindley分布,强度变量服从混合威布尔分布,构建应力-强度模型进行可靠度估计。首先,运用EM算法和Bootstrap方法分别推导得到模型可靠度R的极大似然估计和区间估计,再基于Monte-Carlo模拟及实例数据,运用上述方法对模型的可靠度估计进行分析。结果表明,在偏差意义下,随着样本量的增加,混合威布尔的可靠度估计值逐渐接近真实值。同时,运用混合威布尔分布和单一威布尔分布对Monte-Carlo模拟及实例数据进行拟合分析。结果显示,在AIC信息准则下,混合威布尔分布拟合效果优于单一威布尔分布。

In order to obtain complete failure data and relatively accurate reliability of the product,a stress-strength model is constructed for reliability estimation under progressive type I interval censoring,assuming that the stress and strength variables are independent of each other,the stress variable obeys a Lindley distribution,and the strength variable obeys a mixed Weibull distribution.Firstly,the maximum likelihood estimation and interval estimation of model reliability R are derived by using EM algorithm and Bootstrap method respectively.Then,based on Monte-Carlo simulation and example data,the reliability estimation of the model is analyzed by using the above method.The results show that in the sense of deviation,with the increase of sample size,the reliability estimation value of mixed Weibull gradually approaches the true value.At the same time,the Monte-Carlo simulation and the example data are fitted and analyzed by using the mixed Weibull distribution and the single Weibull distribution.The results show that the fitting effect of the mixed Weibull distribution is better than that of the single Weibull distribution under the AIC information criterion.