基于Bootstrap方法的过程能力指数区间估计

针对传统统计过程控制方法的局限性,利用Bootstrap方法构建了过程能力指数的置信区间,分别对正态分布、指数分布进行仿真计算,对3种Bootstrap置信区间进行了比较。通过实证分析验证了在小样本条件下Bootstrap置信区间的有效性。     

过程能力指数Cpm与合格率的关系

过程能力指数被广泛运用于生产制造领域的质量改进和供应商评估活动.针对Taguchi过程能力指数Cpm虽具有理论优势,但未能在实际生产中广泛运用的问题进行了研究,目的是找出Cpm与合格率之间的关系.运用概率论和数理统计知识,通过公式推导建立了指数Cpm与合格率之间的函数关系,运用MATLAB进行编程计算和图形分析,绘制了Cpm、均值位置和合格率之间的关系图,并提供了参考表格,得出了Taguchi过程能力指数与合格率之间存在对应关系,并与过程输出均值的位置有关的结论,使Taguchi过程能力指数的实际生产中更易于推广.     

非正态过程能力指数估计及抽样方案设计

在实际生产中许多稳定的加工过程不一定满足正态性假设，使得传统的过程能力指数度量失准。为此介绍总结了若干种数据转换方式，将质量特性的分布映射为正态形式，在此基础上再计算过程能力指数。讨论了过程能力指数置信下限与抽样容量、批量产品不合格率之间的对应关系，并给出了非正态分布条件下加工过程抽样方案的设计流程。以某曲轴加工过程为例给出案例分析。     

基于过程能力指数的抽样风险研究

如果将生产过程中上一道工序的加工过程（设备）视为生产者,而紧邻的下一道工序的加工过程（设备）视为使用者,则上道工序加工的零部件在通过质量抽样检验进入下道工序的过程中．就将产生抽样风险。而由抽样风险确定的抽样方案直接关系到加工过程质量控制和检验成本控制等加工效率问题。考虑到许多大批量自动生产线的检验设备已经具备在线计算过程能力指数的能力．提出了一个基于过程能力指数的抽样风险分析方法,通过计算过程能力指数,得到相应的抽样风险．进而确定合理的抽样检验方案,从而将加工过程的重要指标——过程能力指数与抽样检验方案之间建立了联系。最后,以某汽车发动机曲轴生产线加工过程为例进行了抽样风险分析。     

对数正态型元件贮备系统可靠性的置信下限

本文研究了由κ个相互独立的元件和一个转换开关组成的贮备系统.假设元件的寿命服从对数正态分布,转换开关为成败型,本文给出了系统可靠性的表达式、点估计以及Fiducial和Bayes置 信下限.此外,还给出了系统可靠性的点估计以及置信下限的数值计算方法.在小样本情形下, 通过数值比较研究了Fiducial置信下限和Bayes置信下限的覆盖率性质.     

基于不同质量损失函数的过程能力指数比较

通过比较Taguchi过程能力指数Cpm和Cpmk不同于传统的指数Cp和Cpk,指出Taguchi指数反映的是过程输出满足质量损失要求而非合格率的能力;提出均值和标准差变化对不同指数有着不同的影响,指数Cpk比Cpm对标准差的变化更敏感,指数Cpmk对均值的变化最敏感;分析了指数Cpk与合格率的近似对应关系,Taguchi指数与合格率没有确定的一一对应关系,但存在对应区间.通过讨论认为,实践中选用过程能力指数反映了组织的不同质量目标--短期合同要求还是长期"卓越质量".     

基于工序成本的多元过程能力指数分析

单一的多元过程能力指数在反映企业制造多元质量特性产品能力时存在缺陷,无法反映由于各工序成本的差异而造成的工序能力重要性的差别.基于此,从企业工序质量控制和工序成本关系的角度来分析,构建了基于工序成本修正的多元过程能力指数,反映企业的成本控制能力和产品竞争能力.最后,通过修正得到的多元过程能力指数,一方面优选企业的质量改进或控制方案,另一方面判定企业在同类产品制造中的实际质量控制能力和过程成本损失差异.     

过程能力指数和性能指数的若干问题研究

通过对过程能力指数Cpk和过程性能指数Ppk的定义及计算过程的研究,分析Cpk和Ppk的不同,对常用的过程能力指数做出了较为全面的解释,澄清了“Cpk为零就是合格品率为零的”错误观点,并且给出了两种指数的使用范围.     

多批次小批量生产过程能力指数的贝叶斯估计

针对过程能力指数(PCIs)的传统计算方法应用于多批次小批量生产过程出现的失真问题,以多批次小批量生产过程的总体均值和总体方差分别服从共轭正态分布和共轭逆伽马分布,利用共轭贝叶斯估计理论提出了多批次小批量生产过程分布参数估计方法、过程能力指数计算方法及其通用表达式,这种贝叶斯估计方法减小仅用当前批小样本容量估计过程参数...     

过程能力指数在单个实验室能力验证中的应用

以单个实验室能力验证、项目验证结果评价为主要目的，尝试过程能力指数和有偏移情况下的过程能力指数在单个实验室能力验证活动中的实际使用，解决测量审核缺乏综合评价指标的难题。     

Yield‐Related Process Capability Indices for Processes of Multiple Quality Characteristics

Process capability indices (PCIs) have been widely used in industries for assessing the capability of manufacturing processes. Castagliola and Castellanos (Quality Technology and Quantitative Management 2005, 2(2):201–220), viewing that there were no clear links between the definition of the existing multivariate PCIs and theoretical proportion of nonconforming product items, defined a bivariate C_pk and C_p (denoted by BC_pk and BC_p, respectively) based on the proportions of nonconforming product items over four convex polygons for bivariate normal processes with a rectangular specification region. In this paper, we extend their definitions to MC_pk and MC_p for multivariate normal processes with flexible specification regions. To link the index to the yield, we establish a ‘reachable’ lower bound for the process yield as a function of MC_pk. An algorithm suitable for such processes is developed to compute the natural estimate of MC_pk from process data. Furthermore, we construct via the bootstrap approach the lower confidence bound of MC_pk, a measure often used by producers for quality assurance to consumers. As for BC_p, we first modify the original definition with a simple preprocessing step to make BC_p scale‐invariant. A very efficient algorithm is developed for computing a natural estimator of BC_p. This new approach of BC_p can be easily extended to MC_p for multivariate processes. For BC_p, we further derive an approximate normal distribution for , which enables us to construct procedures for making statistical inferences about process capability based on data, including the hypothesis testing, confidence interval, and lower confidence bound. Finally, the proposed procedures are demonstrated with three real data sets. Copyright © 2012 John Wiley & Sons, Ltd.     

Assessing the Proportion of Conformance of a Process from a Bayesian Perspective

A Bayesian technique for assessing the posterior probability that the proportion of conformance of a normally distributed process exceeds a particular value is suggested. Both exact and approximate formulae for the assessment of this probability are derived. Copyright © 2013 John Wiley & Sons, Ltd.     

Comparing Confidence Intervals for Multivariate Process Capability Indices

Multivariate process capability indices (MPCIs) are needed for process capability analysis when the quality of a process is determined by several univariate quality characteristics that are correlated. There are several different MPCIs described in the literature, but confidence intervals have been derived for only a handful of these. In practice, the conclusion about process capability must be drawn from a random sample. Hence, confidence intervals or tests for MPCIs are important. With a case study as a start and under the assumption of multivariate normality, we review and compare four different available methods for calculating confidence intervals of MPCIs that generalize the univariate index C_p. Two of the methods are based on the ratio of a tolerance region to a process region, and two are based on the principal component analysis. For two of the methods, we derive approximate confidence intervals, which are easy to calculate and can be used for moderate sample sizes. We discuss issues that need to be solved before the studied methods can be applied more generally in practice. For instance, three of the methods have approximate confidence levels only, but no investigation has been carried out on how good these approximations are. Furthermore, we highlight the problem with the correspondence between the index value and the probability of nonconformance. We also elucidate a major drawback with the existing MPCIs on the basis of the principal component analysis. Our investigation shows the need for more research to obtain an MPCI with confidence interval such that conclusions about the process capability can be drawn at a known confidence level and that a stated value of the MPCI limits the probability of nonconformance in a known way. Copyright © 2011 John Wiley & Sons, Ltd.     

A New Method for Constructing Confidence Intervals for the Index Cpm

In the statistical literature on the study of the capability of processes through the use of indices, C_pm appears to have been one of the most widely used capability indices and its estimation has attracted much interest. In this article, a new method for constructing approximate confidence intervals or lower confidence limits for this index is suggested. The method is based on an approximation of the non‐central chi‐square distribution, which was proposed by Pearson. Its coverage appears to be more satisfactory compared with that achieved by any of the two most widely used methods that were proposed by Boyles, in situations where one is interested in assessing a lower confidence limit for C_pm. This is supported by the results of an extensive simulation study. Copyright © 2004 John Wiley & Sons, Ltd.