Control Charts for One-sided Capability Indices

There are many industrial product characteristics are desired to be the bigger the best and the smaller the best. The two well-know processes capability indices C _pl and C _pu, which measure larger-the-better and smaller-the-better process capabilities. Obviously, the formulae for the two indices C _pl and C _pu are easy to understand and straightforward to apply. Thus, indices C _pl and C _pu have been utilized by a number of Japanese companies and the U.S. automotive industry by Ford Motor Company. Boyles (1991, Journal of Quality Technology. 23: 17–26) and Spring (1995, Total Quality Management 6(3): 427–438.) point out that as soon as and S control charts are in statistical control, the control charts of process capability indices can be used to monitor the quality of process. In the previous, we know that if the process is not in control, the process capability index control chart can be used to monitor the differences of process capability, and as soon as the process is in control the stable process capability can be identified. Therefore, process capability index control chart not only can be used to monitor the stability of process’s quality but also can be used to monitor the quality of process. Since Boyles (1991, Journal of Quality Technology 23: 17–26.) and Spiring (1995, Total Quality Management 6(1): 21–33.) had had research about control chart of the bilateral specification index C _pm., but there are many kinds of products, which meet unilateral quality specification. Therefore, we will construct the control chart of unilateral specification index C _pl and C _pu to monitor and evaluate the stability of process and process capability.     

Surveillance of the mean behavior of multivariate time series

In this paper several cumulative sum (CUSUM) charts for the mean of a multivariate time series are introduced. We extend the control schemes for independent multivariate observations of crosier [ Technometrics (1988) Vol. 30, pp. 187–194], pignatiello and runger [ Journal of Quality Technology (1990) Vol. 22, pp. 173–186], and ngai and zhang [ Statistica Sinica (2001) Vol. 11, pp. 747–766] to multivariate time series by taking into account the probability structure of the underlying stochastic process. We consider modified charts and residual schemes as well. It is analyzed under which conditions these charts are directionally invariant. In an extensive Monte Carlo study these charts are compared with the CUSUM scheme of theodossiu [ Journal of the American Statistical Association (1993) Vol. 88, pp. 441–448], the multivariate exponentially weighted moving-average (EWMA) chart of kramer and schmid [ Sequential Analysis (1997) Vol. 16, pp. 131–154], and the control procedures of bodnar and schmid [ Frontiers of Statistical Process Control (2006) Physica, Heidelberg]. As a measure of the performance, the maximum expected delay is used.     

我国企业使用过程能力指数情况调查与分析

文章对我国企业使用过程能力指数情况进行了问卷调查。结果显示,我国企业过程能力指数应用中存在的主要问题有：首先,计算过程能力指数的企业不多,且分布不平衡;其次,过程能力指数的可信度不高;再次,不考虑样本的随机性,简单地根据基于样本数据计算的点估计值就给过程的绩效下定论。这些问题的存在,为学者的相关研究提供了视角,也为企业、培训机构、行业协会、有关管理部门开展与过程能力指数有关的活动提供了参考依据。     

Process capability assessment for index C pk based on bayesian approach

Process capability indices have been proposed in the manufacturing industry to provide numerical measures on process reproduction capability, which are effective tools for quality assurance and guidance for process improvement. In process capability analysis, the usual practice for testing capability indices from sample data are based on traditional distribution frequency approach. Bayesian statistical techniques are an alternative to the frequency approach. Shiau, Chiang and Hung (1999) applied Bayesian method to index C_pm and the index C_pk but under the restriction that the process mean μ equals to the midpoint of the two specification limits, m. We note that this restriction is a rather impractical assumption for most factory applications, since in this case C_pk will reduce to C_p. In this paper, we consider testing the most popular capability index C_pk for general situation – no restriction on the process mean based on Bayesian approach. The results obtained are more general and practical for real applications. We derive the posterior probability, p, for which the process under investigation is capable and propose accordingly a Bayesian procedure for capability testing. To make this Bayesian procedure practical for in-plant applications, we tabulate the minimum values of Ĉ_pk for which the posterior probability p reaches desirable confidence levels with various pre-specified capability levels.     

Monitoring processes with changing variances

Statistical process control (SPC) has evolved beyond its classical applications in manufacturing to monitoring economic and social phenomena. This extension has required the consideration of autocorrelated and possibly non-stationary time series. Less attention has been paid to the possibility that the variance of the process may also change over time. In this paper we use the innovations state space modeling framework to develop conditionally heteroscedastic models. We provide examples to show that the incorrect use of homoscedastic models may lead to erroneous decisions about the nature of the process.     

Monitoring the mean and the variance of a stationary process

We deal with the problem of how deviations in the mean or the variance of a time series can be detected. Several simultaneous control charts are introduced which are based on EWMA (exponentially weighted moving average) statistics for the mean and the empirical variance. The combined X − S² EWMA chart is extended to time series. Further simultaneous charts are considered. The comparision of these schemes shows that the residual attempt must be favored if a variance change is present.     

统计过程技术在质量控制中的应用

首先介绍了统计过程控制(简称SPC)的概念,并分析了其在过程质量控制中的重要作用。接着着重阐述了SPC的核心监控工具——控制图及其使用程序。最后提出了企业在实施SPC技术应遵从的步骤以及在实施过程中应注意的问题。     

基于SPC的喷漆线产品质量改善

针对汽车配件制造企业喷漆车间中的喷漆线,应用统计过程控制(SPC)技术对影响喷漆线产品质量的因素进行分析,着重对影响喷漆线产品质量的人为因素进行量化,并建立方程进行研究,找出了影响喷漆线产品质量的主要因素,并提出了相应的改进意见。     

如何分析评价过程能力

文章列出了过程能力指数系列评价公式,阐述了过程能力评价原则和等级评价标准,介绍了过程能力分析方法,并列举了典型案例进行说明。     

有关Cpk公式的12个错误观点剖析

在发现过程能力指数4个基本特性并提出对称公差过程能力指数修正公式Cpk基础上,文章对质量界广为流行的有关Cpk的12个典型错误观点进行了剖析。     

Asymmetric control limits for small samples

When designing control charts, it is usually assumed that the measurement in the subgroups are normally distributed. The assumption of normality implies that the control limits for a chart for sample averages will be symmetrical about the centerline of the chart. However, the assumption of an underlying normal distribution of the data may not hold in some processes. If the measurements are asymmetrically distributed then the decision maker may choose different actions. One thing that can be done is to consider the degree of skewness. If the nature of the underlying distribution is skewed, then the traditional Shewhart individuals chart may not be valid. This paper presents a technique for constructing appropriate asymmetric control limits when the distribution of data cannot be assumed to be a normal distribution. Meanwhile, it proposes a skewness correction method for the generated Burr, lognormal and exponential distributions. Some numerical calculations are generated for n  =  2, 3, 4 by using MATLAB.     

Performance of cumulative sum schemes for monitoring low count-level processes

In many instances attributes data must be used to monitor a manufacturing (or other) process that, in normal conditions, should operate at very low count levels for defects. Lucas (1989) has directed attention to this problem, and has investigated a new control scheme for low count-level processes. An alternative scheme is proposed, based on a Cumulative Sum (CUSUM) of the number (termed Run-Length) of successive samples having zero count-levels between samples having at least one count. Using the criterion of Average Run Length (the average number of samples until a signal is generated) comparisons of the Lucas scheme and the Run-Length CUSUM scheme indicate that ARL values for the Run-Length CUSUM can be up to 50% lower.     

有关过程能力指数基准的若干问题

基准是过程能力指数的一个重要属性,对有关过程能力指数基准的若干问题作出详尽阐述,可为进一步纠正过程能力指数公式错误（诸如Cpk、CpU、CpL等）提供了理论基础。     

Sample size and the Binomial CUSUM Control Chart: the case of 100% inspection

The Binomial CUSUM is used to monitor the fraction defective (p) of a repetitive process, particularly for detecting small to moderate shifts. The number of defectives from each sample is used to update the monitoring CUSUM. When 100% inspection is in progress, the question arises as to how many sequential observations should be grouped together in forming successive samples. The tabular form of the CUSUM has three parameters: the sample size n, the reference value k, and the decision interval h, and these parameters are usually chosen using statistical or economic-statistical criteria, which are based on Average Run Length (ARL). Unlike earlier studies, this investigation uses steady-state ARL rather than zero-state ARL, and the occurrence of the shift can be anywhere within a sample. The principal finding is that there is a significant gain in the performance of the CUSUM when the sample size (n) is set at one, and this CUSUM might be termed the Bernoulli CUSUM. The advantage of using n=1 is greater for larger shifts and for smaller values of in-control ARL. First version: September 1998/Third revision: September 2000     

过程能力指数4个基本特性

根据过程能力指数Cp定义发现了过程能力指数的4个基本特性,即：过程能力指数的对半特性、可计量特性、零判据和基准。这4个特性为研究各种情况下过程能力指数公式提供了理论依据。     

How does improved forecasting benefit detection? An application to biosurveillance

While many methods have been proposed for detecting disease outbreaks from pre-diagnostic data, their performance is usually not well understood. We argue that most existing temporal detection methods for biosurveillance can be characterized as a forecasting component coupled with a monitoring/detection component.In this paper, we describe the effect of forecast accuracy on detection performance. Quantifying this effect allows one to measure the benefits of improved forecasting and determine when it is worth improving a forecast method’s precision at the cost of robustness or simplicity. We quantify the effect of forecast accuracy on detection metrics under different scenarios and investigate the effect when standard assumptions are violated. We illustrate our results by examining performance on authentic biosurveillance data.     

Industrial statistics and its recent contributions to total quality in the Netherlands

The use of statistical methods in quality management has a long history. Most of the pioneers, such as Walter A. Shewhart and W. Edwards Deming, refer to themselves as statisticians. Statistical thinking in industry means that all work is a series of interconnected processes, that all processes show variation, and that a reduction in variation is the key for continuous improvement. In the statistical literature we find several approaches to achieve this: quality by inspection, quality by process control and quality by design. In this paper we give a survey of the contributions of Dutch statisticians during the last five years.     

解读过程能力指数4个基本特性

文章对已发表的过程能力指数4个基本特性的来龙去脉作了详尽的解读,纠正了在过程能力指数理论方面存在的诸多错误认识和观点,对于读者在过程能力指数理论基础上进一步研究探讨多变量过程能力指数具有重要的参考价值。     

SPC技术在多品种小批量数控车削中的应用

针对多品种、小批量生产中,由于样本数据不足而无法直接使用传统SPC(统计过程控制)的问题,构造数据转换模型,将工序相似的质量数据转换为同分布指标,扩大了样本容量,使SPC技术能够方便的应用于多品种、小批量零件的数控车削之中。     

Applied Product Capability Analysis Chart in Measure Step of Six Sigma

This paper will apply product capability analysis chart PCAC in Measure step of Six Sigma. Because the test model is sampling, sampling error must be consider. Thus minimum value will be used to evaluate process capability. Besides the paper used minimum value to evaluate process capability, we also applied the concept of Six Sigma in PCAC and construct PCAC of Six Sigma standard. Finally, PCAC of Six Sigma standard will apply in Six Sigma project of Offset Ratchet Wrenches which manufactured by Y company.