基于Bootstrap-Bayes的加工中心主轴可靠性建模

Reliability modeling of machining center spindle based on Boosttrap-Bayes

针对采用常规Bayes方法对小样本加工中心主轴之类产品进行可靠性建模时与工程实际有较大差异的问题,提出了一种基于Bootstrap-Bayes的小样本可靠性建模方法:为减小先验分布的误差,应用Bootstrap抽样方法对研究对象相同制造环境下同类产品的可靠性模型进行再抽样,从而获得参数的先验分布;在计算后验分布过程中,利用马尔可夫链蒙特卡罗抽样方法,简化了计算,得到了研究对象的可靠性模型。以大样本下经典建模方法所得可靠性模型为基准,与利用Bootstrap-Bayes方法建立的可靠性模型和常规Bayes方法建立的可靠性模型进行比较,结果表明,基于Bootstrap-Bayes的可靠性建模方法所建模型的误差明显小于常规Bayes方法。

The reliability model established using traditional statistical method for the spindle in machining center with small sample size may be biased in the real case. Therefore, a modified reliability modeling method for small sample size was proposed using Bootstrap-Bayes approach. First, the reliability function of time between failures using empirical modeling method was established. Then the accurate of the parameters prior distribution of Bayes method was provided. This method improves the precision of prior distribution built by traditional empirical method. In order to calculate the posterior distribution of parameters, Monte Carlo simulation was developed. Finally, a real-world example of the spindle of one kind of machining center was presented using the proposed approach to show its potential application. The results show that the proposed method can provide an accurate reliability model for small sample failure data.