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.     

Process Capability Indices Based on the Highest Density Interval

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.     

工序能力分析与评价中的几个问题

在工序质量分析与控制中,计算与评价工序能力指数是一项非常重要的工作,也是计算机辅助质量系统的一个重要模块。文章针对目前在工序能力计算与分析中出现的问题,提出了如何合理地进行抽样、样本数据的正态性检验以及对非正态性数据的处理、Ｃｐ的置信区间以及与样本含量的关系,旨在为实际生产过程中质量工程师进行工序能力分析和评价提供指导。     

Evaluation of Nonnormal Process Capability Indices using Generalized Lambda Distribution

Process capability indices (PCIs) are used to describe a manufacturing process expressing its ability to produce items within the specified limits. These indices are developed under the assumption that the underlying process distribution is normal. In industries, there are many manufacturing processes where process distribution can not be described by a normal distribution. In such cases, those PCIs will give misleading results about the process. The most commonly used approach for analysing a nonnormal process data is to fit a standard nonnormal distribution (e.g., weibull, gamma) or a family of distribution curves (e.g., Pearson, Johnson) to the process data and then to estimate the percentile points from the fitted distribution that can be used to compute generalized PCIs. In this article, we outline the procedure using the generalized lambda distribution (GLD) curve for modeling a set of process data and for estimating percentile points in order to compute generalized PCIs. The four-parameter GLD can assume a wide variety of curve shapes and hence it is very useful for the representation of data when the underlying model is unknown. Compared to the Pearson and Johnson family of distributions, the GLD is computationally simpler and more flexible. The article provides all necessary formulas for fitting a GLD curve, estimating its parameters, performing goodness-of-fit tests, and computing generalized PCIs. An example is used to illustrate the calculations that can be easily performed using spreadsheets.     

The New Nino Capability Index for Dynamic Process Capability Analysis

The process capability analysis is a crucial activity to evaluate if the process outcome meets the design specifications. Classically, such analysis is performed by verifying the in‐control condition of the process and evaluating suitable capability indices, by assuming the process in‐control steady‐state condition. However, the in‐control period of the process characterizes only a part of the system functioning cycle, the one with the lower defective rate. In particular, the system functioning cycle is also characterized by the out‐of‐control period, during which a greater defective rate is produced, and such increasing is not considered by the widely adopted capability indices. As consequence, the classical approaches to perform the process capability analysis involves an overestimation of the process capability level. For this reason, in order to overcome the previously described limitation, in the present paper it is proposed a new capability index based on the real defective rate of the process. Thus, such new index is able to estimate the real process capability level. Finally, in order to compare the new index to the conventional C_p capability index, a numerical comparison study related to a process capability analysis is carried out, and the related practical considerations are given. Copyright © 2013 John Wiley & Sons, Ltd.     

Yield‐Based Capability Index for Evaluating the Performance of Multivariate Manufacturing Process

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 EC_pk is proposed based on the idea of six sigma strategy, and there is a one‐to‐one relationship between EC_pk index and process yield. Following the same, idea we propose a PCI MEC_pk to measure processes with multiple characteristics. MEC_pk 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.     

Performance of Multivariate Process Capability Indices Under Normal and Non‐Normal Distributions

In the context of process capability analysis, the results of most processes are dominated by two or even more quality characteristics, so that the assessment of process capability requires that all of them are considered simultaneously. In recent years, many researchers have developed different alternatives of multivariate capability indices using different approaches of construction. In this paper, four of them are compared through the study of their ability to correctly distinguish capable processes from incapable processes under a diversity of simulated scenarios, defining suitable minimum desirable values that allow to decide whether the process meets or does not meet specifications. In this sense, properties analyzed can be seen as sensitivity and specificity, assuming that a measure is sensitive if it can detect the lack of capability when it actually exists and specific if it correctly identifies capable processes. Two indices based on ratios of regions and two based on the principal component analysis have been selected for the study. The scenarios take into account several joint distributions for the quality variables, normal and non‐normal, several numbers of variables, and different levels of correlation between them, covering a wide range of possible situations. The results showed that one of the indices has better properties across most scenarios, leading to right conclusions about the state of capability of processes and making it a recommendable option for its use in real‐world practice. Copyright © 2015 John Wiley & Sons, Ltd.     

On properties of probability-based multivariate process capability indices

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 NMC_pm 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 MC_pm is better as compared with NMC_pm 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.     

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.     

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.     

Multivariate Process Capability Vector Based on One‐Sided Model

To evaluate the capability of manufacturing processes in satisfying the customer's needs, a variety of indices has been developed. Some of them are introduced by researchers to analyse the processes with multivariate quality characteristics. Most of the proposed in the literature multivariate capability indices are defined under assumption of normality distribution of the quality characteristics. Thus, the process region describing the variation of the data has an elliptical shape. In this paper, a multivariate process capability vector with three components is introduced, which allows to access the capability of a process with both normally and non‐normally quality characteristics due to application of a pair of one‐sided models as the process region shape. At the beginning, one‐sided models are defined, next the proposed vector components are proposed and the methodology of their evaluation is presented. The methodology (which in fact could be also applied to both the correlated and non‐correlated characteristics) is verified by applying simulation and real problems. The obtained results show that the proposed methodology performs satisfactorily in all considered cases. Copyright © 2014 John Wiley & Sons, Ltd.     

基于客户满意度的产品感知质量管理

提出了一种基于客户满意的产品感知质量评价方法,利用统计方法建立了评价产品感知质量的感知质量指数;基于此提出了目标建立、目标实施、目标检验的产品感知质量管理方法.     

Comparing Two Process Capability Indices under Balanced One‐Way Random Effect Model

Process capability indices such as C_p, C_pk, C_pmk and C_pm are widely used in manufacturing industries to provide a quantitative measurement of the performance of the products. In this article, we derived generalized confidence intervals for the difference between process capability indices for two processes under one‐way random effect model. Our study provides coverage probability close to the nominal value in almost all cases as shown via simulation. An example from industrial contexts is given to illustrate the results. Copyright © 2012 John Wiley & Sons, Ltd.     

One‐sided Process Capability Assessment in the Presence of Measurement Errors

In the manufacturing industry, many product characteristics are of one‐sided specifications. The well‐known process capability indices C_PU and C_PL are often used to measure process performance. Most capability research works have assumed no measurement errors. Unfortunately, such an assumption is not realistic even if the measurement is conducted using highly sophisticated advanced measuring instruments. Therefore, conclusions drawn regarding process capability are not reliable. In this paper, we consider the estimation and testing of C_PU and C_PL with the presence of measurement errors, to obtain adjusted lower confidence bounds and critical values for true process capability, which can be used to determine whether the factory processes meet the capability requirement when the measurement errors are unavoidable. Copyright © 2005 John Wiley & Sons, Ltd.     

New Insights into the Decisional Use of Process Capability Indices via Hypothesis Testing

Process capability indices C_p, C_pk, and C_pm are still nowadays widely used in industry—thanks to their easy formulation and implementation. This paper aims to give new mathematical insights in order to support their use in decision‐making via hypothesis testing. The minimum sample size usually needed in the applications to achieve fixed significance level and power is reported in light of the new mathematical aspects for C_pk and C_pm, which avoid misleading conclusions and the use of extensive numerical experiments. In addition, power curves for C_pk and C_pm, which have not previously appeared in the literature before, are also presented. Lastly, easy‐to‐follow diagrams for hypothesis testing with C_pk and C_pm and two critical scenarios for C_pm are included in the paper to facilitate the applicative use and the comprehension of the novel inferential aspects. Copyright © 2014 John Wiley & Sons, Ltd.     

On the Implementation of the Principal Component Analysis–Based Approach in Measuring Process Capability

The use of principal component analysis in measuring the capability of a multivariate process is an issue initially considered by Wang and Chen (1998). In this article, we extend their initial idea by proposing new indices that can be used in situations where the specification limits of the multivariate process are unilateral. Moreover, some new indices for multivariate processes are suggested. These indices have been developed so as to take into account the proportion of variance explained by each principal component, thus making the measurement of process capability more effective. Copyright © 2011 John Wiley & Sons, Ltd.     

Multivariate process incapability vector

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.     

基于成本控制的小批量生产工序能力指数研究

传统的工序能力指数分析方法仅仅从统计质量管理的角度对过程能力进行分析,而忽略了所加工产品的不同批量、不同价值、不同加工工序成本的影响。对国内外多品种、小批量的工序能力指数研究现状进行了回顾,在对工序能力指数的点估计及置信区间进行分析的基础上,提出了基于成本控制的多品种、小批量生产方式下确定工序能力指数的方法,从而达到降低生产加工过程成本的目的。