基于Bootstrap抽样的多元过程能力指数估计

Estimation on the Multivariate Process Capability Indices Based on Bootstrap Sampling

过程能力指数主要用于定量描述加工过程满足技术规格要求的能力,目前普遍使用的能力指数如Cp、Cpk、Cpm等主要针对单一质量特性,关于多元质量特性的过程能力指数尚未得到很好地解决。本文首先对多元过程能力指数的发展情况做一总结,指出现存的若干问题,然后在单变量过程服从正态分布的假设下,利用单一质量特性加工过程的差异系数,对单变量过程能力指数进行加权处理,得到多元过程能力指数的计算公式。然后基于Bootstrap抽样技术,对多元过程能力指数的统计分布进行仿真处理,获得了多元能力指数的经验分布及其大致的置信区间,从而为有效进行多元质量特性加工过程分析提供了概率依据。最后以某曲轴加工过程为例给出了应用案例。

The process capability indices （PCIs） are mainly used to describe quantifieationally the capability of the process to satisfy the specifications, and the most widespread PCIs, such as Cp, Cpk, Cpm, etc, are all aiming at univariate quality process primarily, while the PCIs concerning multivariate process （MPCIs） are not yet get to be solved nicely. Firstly, the development of MPCIs is reviewed and some problems that exist in the domain are pointed out. Then, on the assumption that each univeriate process follows a normal distribution, the coettlcients of variance of those processes are used as different weights to synthesize the univariate capability index, and sequentially a new formula for the MPCIs is obtained. And then, by the Bootstrap sampling method, the distributional characteristics of the MPCIs are simulated and estimated, with the confidence intervals of those MPCIs also obtained, which can provide efficient aids to the analysis of multivariate process. Finally an example of axle process is taken for applied analysis.