摘要随着消费者和制造商对产品要求的不断提高，制造过程中的产品质量管理已经变得越来越重要。现代制造业涉及的产品往往包括多个质量特性，多元过程能力指数的研究具有重要的实际意义，是当今学术界的热点问题。一元过程能力指数的研究已经很多，但是多元过程能力指数的研究还存在一些尚未解决的问题。64540

本文利用R软件和Minitab软件，通过仿真分析的方法研究多元过程能力指数。首先介绍了国内外最新的研究情况，以及过程能力指数的基本理论，进而具体阐述了国内外研究较多的四种多元过程能力指数（MCpm、Cpm、MCpc和NMCpm指数）及其优缺点。然后进行了仿真案例分析，从得出的结果验证了相关性对四种过程能力指数的影响。最后，本文总结了这四种指数的性能和适用性，并指出了多元过程能力指数几个值得深入研究的方向：多元过程能力的判断标准问题、基于体积比的多元过程能力指数的改进方向、小样本的多元过程能力指数问题等。

毕业论文关键字  多元过程能力指数；仿真分析；相关性；多元质量特性

毕 业 论 文 外 文 摘 要

Title    Multivariate Capability Indices and   Simulation Study                                                       

Abstract As consumers and manufacturers continuously improve their requirements for the product, quality management of the manufacturing process has become increasingly important. Modern manufacturing products often involve multiple quality characteristics, thus the study of multivariate process capability indices has its own practical significance, which is also a hot issue in today's academia. Univariate process capability indices have received considerable attention, while multivariate process capability indices still have some unsolved problems.

This article studies multivariate process capability indices by simulation analysis method，using the R software and Minitab. Firstly, the basic knowledge of multivariate process capability indices and the latest research on this topic are introduced. Secondly, four multivariate process capability indices are specifically addressed, including their advantages and disadvantages. Thirdly, simulation case study verified the influence from the correlation of the quality characteristics. Finally, the paper presents the conclusion about the performance and applicability of the four indices and points out several directions worthy of further study: criteria of multivariate process capability, suggestion for the modification of multivariate process capability indices based on volume ratio, multivariate process capability indices for small sample.

Keyword  multivariate process capability index；simulation study；correlation；multiple quality characteristics

  目     次

1 绪论 1

  1.1 研究背景与意义 1

  1.2 国内外研究综述 2

  1.3 研究方法与内容 4

2 过程能力指数基本理论 5

  2.1 过程能力分析的基本概念 5

  2.2 一元过程能力指数的定义 7

3 多元过程能力指数 9

  3.1计算多元过程能力指数的几种方法 9

  3.2 多元过程能力指数仿真分析的步骤 15

4 仿真分析