二元Wiener过程下的小样本电主轴可靠性分析
Reliability Analysis of Motorized Spindle with Small Sample based on Two-dimensional Wiener Process

针对高速电主轴产品的退化过程具有多个退化特征量，以及退化过程平稳、缓慢的特点，采用二元Wiener过程对其进行可靠性建模，并将二元Wiener过程的漂移参数看作随机变量来体现电主轴的个体差异性。利用极大似然法结合虚拟增广样本法和Bootstrap法来估计模型中的未知参数，以解决被试电主轴的小样本问题，得到电主轴产品寿命的可靠度函数。最后，通过对2根磨削电主轴产品的退化数据进行比较分析，验证了所提方法的合理性与精确性。
In consideration of the characteristics of high speed motorized spindle product degradation process such as having multiple degradation characteristic variables, and the degradation process being smooth and slow, the two-dimensional Wiener process model was established, in which some unknown parameters were viewed as random variables followed the normal distribution; while the maximum likelihood method combined with virtual augmented samples method and the Bootstrap method which were proposed to solve the problem of small sample were used to estimate the unknown parameters. Then, the resulting product life, the life distribution function and probability density function of reliability function were obtained. Finally, the rationality and accuracy of the method proposed was verified by analyzing the degradation data of two grinding motorized spindles