母体百分位值与百分率置信限的Fiducial推断

Fiducial Inference for Estimating the Confidence Limits of Population's Percentile and Percentage

针对铁道机车车辆现场可靠性数据多为不完全数据的情况,在Fiducial统计理论的基础上,采用Monte Carlo模拟方法建立工程中推断正态分布与威布尔分布母体百分位值与百分率置信限的统计方法。利用约束统计抽样技术,研究基于工程经验限定寿命与可靠性分布参数取值范围的小样本统计推断方法。将传统的确定最大安全寿命的相关系数优化法推广应用到不完全数据信息的情形中,综合利用产品历史共性信息和不完全数据信息进行高精度可靠性评估与寿命预测。与传统频率统计方法或非参数方法相比,用该方法统计推断的结果在大样本与小样本情况下均具有频率意义下的置信限,克服了传统方法在小样本情况下推断精度不高的缺点。

Since incomplete data is often encountered in field reliability data of locomotive and car, methods for estimating the confidence limits of percentile and percentage of normal and Weibull distributions are established by using the Monte Carlo simulation method, which is based on the fiducial statistical inference theory. In addition, the fiducial sampling methods of restricted parameter is developed to solve the small sample problem in condition that the life and reliability＇s parameters are restricted to determined ranges ac- cording to the engineer experience cient optimization method which is or priority information. Besides used to determine the maximum this, the traditional correlation coeffisafety life is extended to the case of incomplete data. Thus, the proposed method can make full use of the similar or the incomplete information, and reach higher precision in both reliability evaluation and life prediction. Compared with the traditional methods, this approach possesses the confidence limits of frequency mean, whether the sample size is relatively big or small. It overcomes the disadvantage of the traditional methods that the inference precision is low with small size sample.