DETECTING EFFECTIVENESS MEASURED BY AURL

This communication addresses the problem of comparing the effectiveness of different control-charting schemes. The measure of average unit run length (AURL) is used to compare the effectiveness of the x-bar charts and the R charts with different sampling frequencies and different sample sizes. Since the trade-off between the frequency of false alarm and the detecting effectiveness is the most critical issue in the design of the control charts, we adjust the control limits of the charts in order to conduct the fair comparisons based on equal frequency of false alarm. © 1997 by John Wiley & Sons, Ltd.     

Practitioner advice: ERLDAT–A web-based tool to design and analyze EWMA control charts

The performance of a control chart is completely characterized by its run length distribution. Quality practitioners usually do not have access to the run length distribution but rely on the average run length (ARL) to design and evaluate the performance of an exponentially weighted moving average (EWMA) control chart. This article presents a web-based tool that provides users easy access to the Phase 2 (online or monitoring phase) run length distribution for a two-sided EWMA control chart with known parameters. The web-based tool calculates the run length distribution, percentiles of the run length distribution, as well as the mean (ARL) and variance (VRL) of the run length distribution. Additional functionality of the web-based tool includes plotting the run length distribution functions, building tables of the quantiles of the run length distribution, finding the smoothing parameter (λ) for an EWMA control chart for fixed control limit that satisfies ARL, VRL or percentile performance, and finding the control chart limit (k) for an EWMA control chart that satisfies ARL, VRL, or percentile performance. This tool and these techniques enable quality practitioners to better design and evaluate EWMA control charts.     

A New Bivariate Control Chart to Monitor the Multivariate Process Mean and Variance Simultaneously

In this article a new control chart which enables a simultaneous monitoring of both the process mean and process variance of a multivariate data will be proposed. A thorough discussion in identifying whether the process mean or variability shifts is also given. Simulation studies will be performed to study the performance of the new chart by means of its average run length (ARL) profiles. Numerous examples are also given to show how the new chart is put to work in real situations.     

Increasing the Sensitivity of Multivariate EWMA Control Chart

A multivariate exponentially weighted moving average (MEWMA) control chart is used for fast detection of small shifts in multivariate statistical quality control. However, for ease of computation, the MEWMA control chart statistics are computed based on the asymptotic form of their covariance matrix in most cases. Another reason that justifies the design of the MEWMA control chart using the asymptotic covariance matrix is that the chart will be insensitive at start-up since processes are more likely to be away from the target value when the control scheme is initiated due to start-up problems. However, if initial out-of-control conditions are deemed important for quick detection, then the MEWMA statistics should be computed based on the exact covariance matrix, as it leads to a natural fast initial response for the MEWMA chart. It will also be shown in this paper the importance of computing the MEWMA statistics based on the exact form of their covariance matrix to further enhance the MEWMA control chart's sensitivity for detecting small shifts. The MEWMA statistics based on the asymptotic and the exact form of their covariance matrix will be referred to as the asymptotic and the exact MEWMA statistics, respectively. Plots and factors that simplify the design of the exact MEWMA control chart are also given.     

Joint Monitoring of Process Mean and Variability with a Single Moving Average Control Chart

Memory based control charts are developed as alternatives to the Shewhart charts for the detection of small sustaining process shifts. Among the widely used memory control charts are the EWMA (Exponentially Weighted Moving Average), CUSUM (Cumulative Sum), and moving average schemes. Relative to the CUSUM chart, the EWMA and moving average charts are quite basic. The EWMA chart uses a weighted average as the chart statistic while the time-weighted moving average chart is based on unweighted moving average. The moving average statistic of width w is simply the average of the w most recent observations. In this article, the use of one moving average control chart to monitor both process mean and variability. This new moving average chart is efficient in detecting both increases and decreases in mean and/or variability.     

过程能力指数与不合格品率的关系模型

传统Shewhart-p控制图只对单一属性的不合格品率进行监控,在过程发生偏移时有一定的滞后性。为提高不合格品率控制图的精度,提出一种多元指数加权移动平均不合格品率 (multivariate exponentially weighted moving average p, MEWMA-p)控制图。该控制图将多个属性的不合格品率应用于多元指数加权移动平均控制图,可同时对多个属性进行监控,并且对于小范围的偏移更加敏感。对比分析同等偏移程度下指数加权移动平均不合格品率 (exponentially weighted moving average p, EWMA-p) 控制图与MEWMA-p控制图的平均运行长度 (average run length, ARL) 结果,并通过模拟仿真说明该方法的有效性。

     

Design and implementation of CUSUM exceedance control charts for unknown location

Nonparametric control charts provide a robust alternative in practice when the form of the underlying distribution is unknown. Nonparametric CUSUM (NPCUSUM) charts blend the advantages of a CUSUM with that of a nonparametric chart in detecting small to moderate shifts. In this paper, we examine efficient design and implementation of Phase II NPCUSUM charts based on exceedance (EX) statistics, called the NPCUSUM-EX chart. We investigate the choice of the order statistic from the reference (Phase I) sample that defines the exceedance statistic. We see that choices other than the median, such as the 75th percentile, can yield improved performance of the chart in certain situations. Furthermore, observing certain shortcomings of the average run-length, we use the median run-length as the performance metric. The NPCUSUM-EX chart is compared with the NPCUSUM-Rank chart based on the popular Wilcoxon rank-sum statistic. We also study the choice of the reference value, k, of the CUSUM charts. An illustration with real data is provided.