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1.
    
《Quality Engineering》2012,24(3):290-299
ABSTRACT

Process Capability Indices, such as Cp and Cpk have been widely used as statistical tools to assess the manufacturing process performance. These indices provide numerical measures on process precision, process accuracy and process performance. Extensive researches have been done on the univariate process capability indices in the last two decades. However, process capability indices for processes with multiple quality characteristics have received little attention, comparatively. The multivariate process capability indices, which are used for evaluation of processes with correlated quality characteristics such as weight, height and width, could be investigated, in depth. In this research the concept of process capability and its relevant indices in univariate and multivariate cases are discussed. Based on the previous works, a new multivariate process capability vector (NMPCV) is introduced. This vector is based on a modification of the traditional multivariate process capability indices. The value and the power of this new index are evaluated using field and simulated data. The results of this research show that NMPCV is a better tool for judging the process accuracy, the process precision and the process performance. When the characteristics are highly correlated, the results are much better.  相似文献   

2.
    
Process capability indices (PCIs) have been widely used in the manufacturing industry providing numerical measures on process precision, accuracy and performance. Capability indices measures for processes with a single characteristic have been investigated extensively. However, an industrial product may have more than one quality characteristic. In order to establish performance measures for evaluating the capability of a multivariate manufacturing process, multivariate PCIs should be introduced. In this paper, we analyze the relationship between PCI and process yield. The PCI ECpk is proposed based on the idea of six sigma strategy, and there is a one‐to‐one relationship between ECpk index and process yield. Following the same, idea we propose a PCI MECpk to measure processes with multiple characteristics. MECpk index can evaluate the overall process yield of both one‐sided and two‐sided processes. We also analyze the effect of covariance matrix on overall process yield and suggest a solution for improving overall process yield. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

3.
    
Multivariate process capability indices (MPCIs) have been proposed to measure multivariate process capability in real-world application over the past three decades. For the practitioner's point of view, the intention of this paper is to examine the performances and distributional properties of probability-based MPCIs. Considering issues of construction of capability indices in multivariate setup and computation with performance, we found that probability-based MPCIs are a proper generalization of univariate basic process capability indices (PCIs). In the beginning of this decade, computation of probability-based indices was a difficult and time-consuming task, but in the computer age statistics, computation of probability-based MPCIs is simple and quick. Recent work on the performance of MPCI NMCpm and distributional properties of its estimator reasonably recommended this index, for use in practical situations. To study distributional properties of natural estimators of probability-based MPCIs and recommended index estimator, we conducted simulation study. Though natural estimators of probability-based indices are negatively biased, they are better with respect to mean, relative bias, mean square error. Probability-based MPCI MCpm is better as compared with NMCpm with respect to performance and as its estimator quality. Hence, in real-world practice, we recommend probability-based MPCIs as a multivariate analogue of basic PCIs.  相似文献   

4.
    
Process capability indices evaluate the capability of the processes in satisfying customer's requirements. This paper introduces a superstructure multivariate process incapability vector for multivariate normal processes and then, compares it with four recently proposed multivariate process capability indices to show its better performance. In addition, the effects of two modification factors are investigated. Also, bootstrap confidence intervals for the first component of the proposed vector are obtained. Furthermore, real manufacturing data sets are presented to demonstrate the applicability of the proposed vector.  相似文献   

5.
    
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 Cp. 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.  相似文献   

6.
A process capability index is a measure that evaluates the behavior of a product or process characteristics related to the engineering specification. In the literature, many articles can be found about capability indices for both symmetric and asymmetric tolerance. In this article, we introduce a new class of indices, C′′′p(u, v), for the processes with asymmetric tolerance. In addition, we study the relation between this index and the departure ratio of the process centering, as well as, the relation between this index and the upper bound of the percentage of non-conforming products. Based on these results we suggest a criteria for choosing an index from the under investigation class. To guide practitioners, numerical examples are provided.  相似文献   

7.
    
Often the quality of a process is determined by several correlated univariate variables. In such cases, the considered quality characteristic should be treated as a vector. Several different multivariate process capability indices (MPCIs) have been developed for such a situation, but confidence intervals or tests have been derived for only a handful of these. In practice, the conclusion about process capability needs to be drawn from a random sample, making confidence intervals or tests for the MPCIs important. Principal component analysis (PCA) is a well‐known tool to use in multivariate situations. We present, under the assumption of multivariate normality, a new MPCI by applying PCA to a set of suitably transformed variables. We also propose a decision procedure, based on a test of this new index, to be used to decide whether a process can be claimed capable or not at a stated significance level. This new MPCI and its accompanying decision procedure avoid drawbacks found for previously published MPCIs with confidence intervals. By transforming the original variables, we need to consider the first principal component only. Hence, a multivariate situation can be converted into a familiar univariate process capability index. Furthermore, the proposed new MPCI has the property that if the index exceeds a given threshold value the probability of non‐conformance is bounded by a known value. Properties, like significance level and power, of the proposed decision procedure is evaluated through a simulation study in the two‐dimensional case. A comparative simulation study between our new MPCI and an MPCI previously suggested in the literature is also performed. These studies show that our proposed MPCI with accompanying decision procedure has desirable properties and is worth to study further. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

8.
    
The purpose of this paper is to provide a multivariate process capability index, which could be used regardless on data distribution and also on data correlation. Such an index could be defined because of application of non‐parametric methodology that utilizes a data depth concept. Based on this concept, a two‐phase methodology was developed. In the first phase the modified tolerance region is estimated, while in the second one, a current process is assessed using the proposed three‐component index. Estimation of a modified tolerance region on the basis on historical data allows applying the methodology not only for bilateral quality characteristics but also for unilateral ones, where often in practice, the modified tolerance region could be defined as a closed region. The performance of the proposed index was evaluated using bilateral and unilateral examples. The obtained results showed that the proposed index performs satisfactorily for all the considered cases. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

9.
    
Conventional process capability analysis is used to measure and control the quality level of a production process in real exercises for on-line quality management. There has been a deficiency in this type of management; namely, the defects which occur in the production process are only passively detected and modified afterwards. Additionally, conventional process capability expression has difficulty distinguishing between alternatives for process selection among possible candidates before process realisation. There is, therefore, considerable motivation for developing a process capability expression which can be used to evaluate alternatives at the beginning of the process design, i.e., off-line application. The conventional Cpm expression is built up by measuring mean deviation and process variances for on-line application. However, if Cpm is used for the process capability analysis for process design, an erroneous Cpm value is found and an inappropriate process design is ended. Thus, the proposed process capability expression revised from the conventional Cpm in consideration of the balance between tolerance cost and quality loss has been developed. This development is the main contribution of this research and, with this development, the appropriate mean and tolerance values can be determined simultaneously prior to the real production process so as to maximise the proposed process capability value. The production is then processed with the pre-determined mean and tolerance values in a real production process. The expectation after process realisation is that the produced responses will be the best of all the alternatives in terms of quality and cost, and that the process capability value obtained after the real production process will be close to the proposed process capability value maximised prior to the real production process.  相似文献   

10.
    
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 Cpk and Cp (denoted by BCpk and BCp, 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 MCpk and MCp 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 MCpk. An algorithm suitable for such processes is developed to compute the natural estimate of MCpk from process data. Furthermore, we construct via the bootstrap approach the lower confidence bound of MCpk, a measure often used by producers for quality assurance to consumers. As for BCp, we first modify the original definition with a simple preprocessing step to make BCp scale‐invariant. A very efficient algorithm is developed for computing a natural estimator of BCp. This new approach of BCp can be easily extended to MCp for multivariate processes. For BCp, 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.  相似文献   

11.
    
For many quality characteristics, such as circularity, cylindricity, straightness and flatness, positive skewness in the inspection data is the norm, and, in fact, is desirable. Summarizing the process performance using such data in conjunction with capability indices has recently received a considerable amount of attention, with new indices being proposed and compared for usefulness and accuracy. This paper is intended to contribute to this growing discussion, and to add a unique focus. In particular, this investigation concentrates on one form of a neoclassical index, the Cs index, originally proposed to be sensitive to skewness and to decrease in value as the skewness increased in the underlying distribution of the data. In other words, ‘skewness is badness’. Looking at this index from an altered perspective, the possibility that this index could serve a useful purpose in summarizing process performance for such non‐normal processes by merely changing its interpretation or slightly changing its form is considered. Hence, actual data from circularity measurements are used to identify a relevant group of distributions, and then the accuracy of Cs is investigated along with its modified version for this group of distributions. In particular, this investigation includes several Rayleigh and gamma distributions for various sample sizes and reports on the bias of the proposed estimators. These findings indicate that such a modified index has some useful attributes in reflecting process performance, with respect to the percentage of non‐conformance and the accuracy for relatively large samples. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

12.
基于不同质量损失函数的过程能力指数比较   总被引：1，自引：0，他引：1  
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".  相似文献   

13.
    
Two problems greatly affect the use of capability indices such as , and : the lack of affinity with the process fraction defective π and the difficulty of dealing with the sampling distributions of their natural estimators. In this paper, a capability index which is in one‐to‐one correspondence with π is introduced and simple inferential procedures under a Bayesian perspective are developed to facilitate its use in industrial applications. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

14.
过程能力指数Cpm与合格率的关系   总被引：1，自引：0，他引：1  
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.  相似文献   

15.
    
Process capability indices (PCIs) are used in statistical process control to evaluate the capability of the processes in satisfying the customer's needs. In the past two decades varieties of PCI are introduced by researchers to analyze the process capability with univariate or multivariate quality characteristics. To the best of our knowledge, most famous multivariate capability indices are proposed when the quality characteristics have both upper and lower specification limits. These indices are incapable to assess the multivariate processes capability with unilateral specification. In this article, we propose a new multivariate PCI to analyze the processes with one or more unilateral specification limits. This new index also accounts for all problems in the best PCIs of the literature. The performance of the proposed index is evaluated by real cases under different situations. The results show that the proposed index performs satisfactorily in all cases considered. Copyright © 2012 John Wiley & Sons, Ltd.  相似文献   

16.
基于工序成本的多元过程能力指数分析   总被引：1，自引：0，他引：1  
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.  相似文献   

17.
    
Process capability indices (PCIs) have been frequently employed in manufacturing organizations. In this paper, some existing PCIs are reviewed, and after that, the loss function concept is used as a practical tool for PCI. In this regard, an effective scheme for a revised PCI is presented. The preference of the revised index is presented in theory and illustrated through a numerical example. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

18.
    
For process capability indices (PCIs) of non‐normal processes, the natural tolerance is defined as the difference between the 99.865 percentile and the 0.135 percentile of the process characteristic. However, some regions with relatively low probability density may still be included in this natural tolerance, while some regions with relatively high probability density may be excluded for asymmetric distributions. To take into account the asymmetry of process distributions and the asymmetry of tolerances from the viewpoint of probability density, the highest density interval is utilized to define the natural tolerance, and a family of new PCIs based on the highest density interval is proposed to ensure that regions with high probability density are included in the natural tolerance. Some properties of the proposed PCIs and two algorithms to compute the highest density interval are given. A real example is given to show the application of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   

19.
    
Generally, an industrial product has more than one quality characteristic. In order to establish performance measures for evaluating the capability of a multivariate manufacturing process, several multivariate process capability indices have been developed in the past few years. Among them, Taam's MCp and MCpm indices have the drawback of overestimation and Hubele's three‐component capability vector lacks simplicity in practice. In this article, taking the correlation among multiple quality characteristics into account, we develop two novel indices; NMCp and NMCpm. Using two numerical examples we demonstrate that the true performance of multivariate processes are accurately reflected in our NMCp and NMCpm indices and in their associated interval estimates. Finally, simulation results show that our indices outperform both those of Taam and Hubele. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

20.
过程能力指数和性能指数的若干问题研究   总被引：4，自引：3，他引：4  
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.  相似文献   

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