用自助加权范数法评估三参数威布尔分布可靠性最优置信区间

Assessment of optimum confidence interval of reliability with three-parameter Weibull distribution using bootstrap weighted-norm method

提出自助加权范数法,以评估三参数威布尔分布可靠性的最优置信区间.基于可靠性经验值与理论值的差异,通过6个最小加权范数准则,构建出威布尔分布的最优参数信息向量.对最优参数信息向量进行自助再抽样,获得生成参数信息向量,用于模拟参数的概率密度函数.在给定置信水平下,求解出参数的估计真值及其置信区间,并据此建立可靠性的估计真值函数及其最优置信区间函数.滚动轴承性能寿命案例、直升机部件失效案例与某试件疲劳寿命案例的研究表明:使用自助加权范数法,估计真值函数与可靠性经验值相一致,最优置信区间函数能描述试验结果的真实状态.

The bootstrap weighted-norm method was proposed to evaluate the optimum confidence interval of reliability with three-parameter Weibull distribution.Based on the difference between the empirical values and the theoretical values of reliability,an information vector of the optimum parameters of the Weibull distribution was structured in the light of six criterions of the minimum weighted-norm.By bootstrap resampling the information vector of the optimum parameters,a generated information vector was obtained to simulate the probability density function of the parameters.The estimated truth-value and its confidence interval of the parameters were solved and the estimated truth-value function and its optimum confidence interval function of the reliability could accordingly be established under the given confidence level.The case studies of the rolling bearing performance life,the helicopter component failure and the specimen fatigue life indicate that the estimated truth-value function is in accord with empirical values of reliability by using bootstrap weighted-norm method,and the optimum confidence interval function is able to describe true state of the test results.