标题: 非对称规格区间之制程能力指标的统计性质
Statistical Properties of the Estimated Capability Indices for Processes with Asymmetric Tolerances
作者: 林碧川
P. C. Lin
彭文理
W. L. Pearn
工业工程与管理学系
关键字: 制程能力指标;非对称规格区间;目标值;制程良率;制程损失;遵循常态分配之制程;Process capability index;Asymmetric tolerances;Target value;Process yield;Process loss;Normally distributed process
公开日期: 1999
摘要: 制程能力指标 (Process Capability Index) 是一个衡量制程绩效的方便工具,可以藉其指标的数值来评估制程,以了解此制程的产出,合乎预设规格的程度。近来,关于制程能力指标的研究工作,散见于统计与品管相关的文献中。大部份的研究均着重于规格区间为对称的情况,当产品规格区间为非对称的情况时,是一般研究者较为忽略的。Pearn and Chen (1998) 提出能力指标 Cpk" 来处理非对称规格区间之制程,新指标 Cpk" 为指标 Cpk 的推广。本文首先在常态分配之假设下,推导出 Cpk" 的估计量的累积分配函数与机率密度函数,便于作区间估计、统计假设检定等进一步的统计分析。随之,将建构指标 Cpk" 的相同理念,应用到能力指标 Cpm 与 Cpmk,分别发展出新指标 Cpm" 与 Cpmk"。我们分别将这些新指标与文献中现有的指标加以比较。在常态分配之假设下,我们分别推导出 Cpm" 与 Cpmk" 的估计量的累积分配函数与机率密度函数,也分别探讨了 Cpm" 与 Cpmk" 的估计量的统计性质。
Process capability indices (PCIs), providing numerical measures of whether or not the ability of a manufacturing process meets a preset level of production tolerance, are considered as a practical tool in industry. Capability indices have received much interest in the statistical literature during recent years. Most research work, however, have focused on developing and investigating PCIs for processes with symmetric tolerances. There have been relatively few papers published dealing specially with the case when the tolerances are asymmetric. Pearn and Chen (1998) proposed a new generalization of index Cpk, called Cpk", to handle processes with asymmetric tolerances. In this dissertation, we derive the cumulative distribution function and the probability density function of the estimated index of Cpk" when sampling from a normal distribution. The explicit form of the distribution of the estimated indices under investigation could be viewed as an interesting and useful result in interval estimation and testing statistical hypothesis. Based on the same idea, we consider new generalizations of indices Cpm and Cpmk, called Cpm" and Cpmk", respectively. We make a comprehensive study of several proposed indices for asymmetric tolerances. We derive the explicit forms of the cumulative distribution functions and the probability density functions of the estimators of Cpm" and Cpmk" when sampling from a normal distribution to increase the utility of these capability indices. We also investigate the statistical properties of the natural estimators of Cpm" and Cpmk" assuming the process is normally distributed.
Abstract
List of Contents
List of Figures
List of Tables
Chapter 1. Introduction
Chapter 2. A New Generalization of Cpk
2.1 Introduction
2.2 Distribution of the Estimated Cpk"
Chapter 3. A New Generalization of Cpm
3.1 Introduction ∙
3.2 Existing Generalizations
3.3 A New Generalization Cpm"
3.4 Estimation of Cpm" and the Sampling Distribution
3.5 Conclusions
Chapter 4. A New Generalization of Cpmk
4.1 Introduction
4.2 Existing Generalizations
4.3 A New Generalization Cpmk"
4.4 Estimation of Cpmk" and the Sampling Distribution
4.5 Conclusions
Appendix A
Appendix B
References
URI: http://140.113.39.130/cdrfb3/record/nctu/#NT880031005
http://hdl.handle.net/11536/65163
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