A Multivariate Exponentially Weighted Moving Average Control Chart

A multivariate extension of the exponentially weighted moving average (EWMA) control chart is presented, and guidelines given for designing this easy-to-implement multivariate procedure. A comparison shows that the average run length (ARL) performance of this chart is similar to that of multivariate cumulative sum (CUSUM) control charts in detecting a shift in the mean vector of a multivariate normal distribution. As with the Hotelling's χ² and multivariate CUSUM charts, the ARL performance of the multivariate EWMA chart depends on the underlying mean vector and covariance matrix only through the value of the noncentrality parameter. Worst-case scenarios show that Hotelling's χ² charts should always be used in conjunction with multivariate CUSUM and EWMA charts to avoid potential inertia problems. Examples are given to illustrate the use of the proposed procedure.     

A New Hybrid Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean: Discussion

A new hybrid exponentially weighted moving average (HEWMA) control chart has been proposed in the literature for efficiently monitoring the process mean. In that paper, the computed variance of the HEWMA statistic was, unfortunately, not correct! In this discussion, the correct variance of the HEWMA statistic is given, and the run length characteristics of the HEWMA control chart are studied and explored. It is noticed that not only the superiority of the HEWMA control chart remains over the existing (considered before) charts but also the new results based on the corrected control limits are more profound and reflective. Copyright © 2016 John Wiley & Sons, Ltd.     

Control charts for positively‐skewed populations with weighted standard deviations

This paper proposes a heuristic method of constructing , cumulative sum and exponentially weighted moving average control charts for skewed populations with weighted standard deviations obtained by decomposing the standard deviation into upper and lower deviations adjusted in accordance with the direction and degree of skewness. These control charts, however, reduce to standard control charts when the underlying distribution is symmetric. Simple formulae are derived to estimate unknown process parameters from means and ranges of subgroups. The false alarm rates of these control charts are compared with those of existing control charts when the underlying distribution is Weibull, gamma, or lognormal. Simulation results show that considerable improvement over the existing methods can be achieved when the underlying distribution is skewed. Copyright © 2001 John Wiley & Sons, Ltd.     

A Reevaluation of the Adaptive Exponentially Weighted Moving Average Control Chart When Parameters are Estimated

The performance of control charts can be adversely affected when based on parameter estimates instead of known in‐control parameters. Several studies have shown that a large number of phase I observations may be needed to achieve the desired in‐control statistical performance. However, practitioners use different phase I samples and thus different parameter estimates to construct their control limits. As a consequence, there would be in‐control average run length (ARL) variation between different practitioners. This kind of variation is important to consider when studying the performance of control charts with estimated parameters. Most of the previous literature has relied primarily on the expected value of the ARL (AARL) metric in studying the performance of control charts with estimated parameters. Some recent studies, however, considered the standard deviation of the ARL metric to study the performance of control charts. In this paper, the standard deviation of the ARL metric is used to study the in‐control and out‐of‐control performance of the adaptive exponentially weighted moving average (AEWMA) control chart. The performance of the AEWMA chart is then compared with that of the Shewhart and EWMA control charts. The simulation results show that the AEWMA chart might represent a good solution for practitioners to achieve a reasonable amount of ARL variation from the desired in‐control ARL performance. In addition, we apply a bootstrap‐based design approach that provides protection against frequent false alarms without deteriorating too much the out‐of‐control performance. Copyright © 2014 John Wiley & Sons, Ltd.     

A Robust Bivariate Control Chart Alternative to the Hotelling's T2 Control Chart

In this paper, we proposed a new bivariate control chart denoted by based on the robust estimation as an alternative to the Hotelling's T² control chart. The location vector and the variance‐covariance matrix for the new control chart are obtained using the sample median, the median absolute deviation from the sample median, and the comedian estimator. The performance of the proposed method in detecting outliers is evaluated and compared with the Hotelling's T² method using a Monte‐Carlo simulation study. A numerical example is considered to illustrate the application of the proposed method. Copyright © 2012 John Wiley & Sons, Ltd.     

A 2‐Stage Attribute‐Variable Control Chart to Monitor a Vector of Process Means

The aim of this paper is to propose a combined attribute‐variable control chart, namely M a x D  ? T ², to monitor a vector of process means μ  = [μ ₁,…,μ _q ] in a multivariate process control. The procedure consists of splitting a sample of size n into two sub‐samples of sizes n ₁ and n ₂(n  = n ₂ + n ₂), determined by an optimized process. Units of the first sub‐sample are evaluated by an attribute inspection. Using a device like a gauge ring, each unit of the first sub sample is considered approved related to the quality characteristic i if X _i ∈[ ; ]; otherwise, it is disapproved in the characteristic i , where and (obtained by an optimization) are respectively the lower and upper discriminating limits of the quality dimension X _i . If the number of disapproved items in any quality characteristic is higher than a control limit, then the measurement of the q quality characteristics is taken on each unit of the second sub‐sample and the statistic T ² is calculated. If T ² < L (L , the control limit) the process is judged as in control. The process will suffer intervention if both charts signal. The procedure has an advantage to not inspect the units of the second sub‐sample if the first sub‐sample indicates that the process is in control. This proposal shows a better performance than T ² control chart for a large number of scenarios. The two control limits and discriminant limits are optimized to reach a desired value of A R L ₀ and to minimize A R L ₁. Copyright © 2017 John Wiley & Sons, Ltd.     

A Robust Control Chart

This article studies alternative standard deviation estimators that serve as a basis to determine the control chart limits used for real‐time process monitoring (phase II). Several existing (robust) estimation methods are considered. In addition, we propose a new estimation method based on a phase I analysis, that is, the use of a control chart to identify disturbances in a data set retrospectively. The method constructs a phase I control chart derived from the trimmed mean of the sample interquartile ranges, which is used to identify out‐of‐control data. An efficient estimator, namely the mean of the sample standard deviations, is used to obtain the final standard deviation estimate from the remaining data. The estimation methods are evaluated in terms of their mean squared errors and their effects on the performance of the phase II control chart. It is shown that the newly proposed estimation method is efficient under normality and performs substantially better than standard methods when disturbances are present in phase I. Copyright © 2012 John Wiley & Sons, Ltd.     

Design Strategies for the Multivariate Exponentially Weighted Moving Average Control Chart

The multivariate exponentially weighted moving average (MEWMA) control chart has received significant attention from researchers and practitioners because of its desirable properties. There are several different approaches to the design of MEWMA control charts: statistical design; economic–statistical design; and robust design. In this paper a review and comparison of these design strategies is provided.Copyright © 2004 John Wiley & Sons, Ltd.     

Process capability indices for skewed populations

This paper proposes a new method of constructing process capability indices (PCIs) for skewed populations. It is based on a weighted standard deviation method which decomposes the standard deviation of a quality characteristic into upper and lower deviations and adjusts the value of the PCI using decomposed deviations in accordance with the skewness estimated from sample data. For symmetric populations, the proposed PCIs reduce to standard PCIs. The performance of the proposed PCIs is compared with those of standard and other PCIs, and finite sample properties of the estimates are investigated using Monte Carlo simulation. Numerical studies indicate that considerable improvements over existing methods can be achieved by the use of the weighted standard deviation method when the underlying distribution is skewed. Copyright © 2002 John Wiley & Sons, Ltd.     

An Improved Maximum Exponentially Weighted Moving Average Control Chart for Monitoring Process Mean and Variability

Maximum exponentially weighted moving average (MaxEWMA) control charts have gained considerable attention for detecting changes in both process mean and process variability. In this paper, we propose an improved MaxEWMA control charts based on ordered ranked set sampling (ORSS) and ordered imperfect ranked set sampling (OIRSS) schemes for simultaneous detection of both increases and decreases in the process mean and/or variability, named MaxEWMA‐ORSS and MaxEWMA‐OIRSS control charts. These MaxEWMA control charts are based on the best linear unbiased estimators of location and scale parameters obtained under ORSS and OIRSS methods. Extensive Monte Carlo simulations have been used to estimate the average run length and standard deviation of run length of the proposed MaxEWMA control charts. These control charts are compared with their counterparts based on simple random sampling (SRS), that is, MaxEWMA‐SRS and MaxGWMA‐SRS control charts. The proposed MaxEWMA‐ORSS and MaxEWMA‐OIRSS control charts are able to perform better than the MaxEWMA‐SRS and MaxGWMA‐SRS control charts for detecting shifts in the process mean and dispersion. An application to real data is provided to illustrate the implementation of the proposed MaxEWMA control charts. Copyright © 2013 John Wiley & Sons, Ltd.     

测量标准因素判定(x)控制图异常导致标准核查不通过的分析

依据GB/T27025-2008《检测和校准实验室能力的通用要求》,计量技术机构应开展测量标准核查,休哈特控制图是标准核查工作的主要方法.本文简要介绍了基于休哈特控制图理论的标准核查方法,对测量标准因素引起的三种控制图异常进行了深入讨论,对异常原因进行了追溯,分析了测量标准可能存在的问题,并给出了排除失控因素的建议.     

Robust Multivariate Control Chart for Outlier Detection Using Hierarchical Cluster Tree in SW2

The goal of this paper is to develop a new multivariate control chart that can effectively detect potential outlier(s) in multi‐dimensional data while keeping the masking and swamping effects under control. The hierarchical clustering tree plays a central role in the proposed control chart, in an attempt to improve the Sullivan and Woodall's second method, known as the SW2 method. Historical multivariate datasets taken from the literature are used as the benchmarks to illustrate the performance of the proposed control charts in comparison to nine existing methods for outlier detection. The two criteria, the masking and swamping rates, are used as yardsticks for the evaluation purpose. An additional simulation study by means of Monte Carlo experiments further verifies that the proposed control chart that incorporates the hierarchical clustering tree performs much better in outlier detection and swamping prevention than the original SW2 and minimum volume ellipsoid methods. Copyright © 2012 John Wiley & Sons, Ltd.     

A New Exponentially Weighted Moving Average Control Chart for Monitoring Process Dispersion

Exponentially weighted moving average (EWMA) control charts have been widely recognized as an advanced statistical process monitoring tool due to their excellent performance in detecting small to moderate shifts in process parameters. In this paper, we propose a new EWMA control chart for monitoring the process dispersion based on the best linear unbiased absolute estimator (BLUAE) obtained under paired ranked set sampling (PRSS) scheme, which we name EWMA‐PRSS chart. The performance of the EWMA‐PRSS chart is evaluated in terms of the average run length and standard deviation of run length, estimated using Monte Carlo simulations. These control charts are compared with their existing counterparts for detecting both increases and decreases in the process dispersion. It is observed that the proposed EWMA‐PRSS chart performs uniformly better than the EWMA dispersion charts based on simple random sampling and ranked set sampling (RSS) schemes. We also construct an EWMA chart based on imperfect PRSS (IPRSS) scheme, named EWMA‐IPRSS chart, for detecting overall changes in the process variability. It turns out that, with reasonable assumptions, the EWMA‐IPRSS chart outperforms the existing EWMA dispersion charts. A real data set is used to explain the construction and operation of the proposed EWMA‐PRSS chart. Copyright © 2014 John Wiley & Sons, Ltd.     

A New Exponentially Weighted Moving Average Control Chart for Monitoring the Process Mean

Exponentially weighted moving average (EWMA) quality control schemes have been recognized as a potentially powerful process monitoring tool because of their superior speed in detecting small to moderate shifts in the underlying process parameters. In quality control literature, there exist several EWMA charts that are based on simple random sampling (SRS) and ranked set sampling (RSS) schemes. Recently, a mixed RSS (MxRSS) scheme has been introduced, which encompasses both SRS and RSS schemes, and is a cost‐effective alternative to the RSS scheme. In this paper, we propose new EWMA control charts for efficiently monitoring the process mean based on MxRSS and imperfect MxRSS (IMxRSS) schemes, named EWMA–MxRSS and EWMA–IMxRSS charts, respectively. Extensive Monte Carlo simulations are used to estimate the run length characteristics of the proposed EWMA charts. The run length performances of the suggested EWMA charts are compared with the classical EWMA chart based on SRS (EWMA–SRS). It turns out that both EWMA–MxRSS and EWMA–IMxRSS charts perform uniformly better than the EWMA–SRS chart when detecting all different shifts in the process mean. An application to a real data set is provided as an illustration of the design and implementation of the proposed EWMA chart. Copyright © 2014 John Wiley & Sons, Ltd.     

A Robust Phase I Exponentially Weighted Moving Average Chart for Dispersion

A Phase I estimator of the dispersion should be efficient under in‐control data and robust against contaminations. Most estimation methods proposed in the literature are either efficient or robust against either sustained shifts or scattered disturbances. In this article, we propose a new estimation method of the dispersion parameter, based on exponentially weighted moving average charting, which is efficient and robust to both types of unacceptable observations in Phase I. We compare the method with various existing estimation methods and show that the proposed method has the best overall performance if it is unknown what type of contaminations are present in Phase I. We also study the effect of the robust estimator from Phase I on the Phase II exponentially weighted moving average control chart performance. Copyright © 2014 John Wiley & Sons, Ltd.     

The Effect of Autocorrelation on the Hotelling T2 Control Chart

One of the basic assumptions for traditional univariate and multivariate control charts is that the data are independent in time. For the latter, in many cases, the data are serially dependent (autocorrelated) and cross‐correlated because of, for example, frequent sampling and process dynamics. It is well known that the autocorrelation affects the false alarm rate and the shift‐detection ability of the traditional univariate control charts. However, how the false alarm rate and the shift‐detection ability of the Hotelling T² control chart are affected by various autocorrelation and cross‐correlation structures for different magnitudes of shifts in the process mean is not fully explored in the literature. In this article, the performance of the Hotelling T² control chart for different shift sizes and various autocorrelation and cross‐correlation structures are compared based on the average run length using simulated data. Three different approaches in constructing the Hotelling T² chart are studied for two different estimates of the covariance matrix: (i) ignoring the autocorrelation and using the raw data with theoretical upper control limits; (ii) ignoring the autocorrelation and using the raw data with adjusted control limits calculated through Monte Carlo simulations; and (iii) constructing the control chart for the residuals from a multivariate time series model fitted to the raw data. To limit the complexity, we use a first‐order vector autoregressive process and focus mainly on bivariate data. © 2014 The Authors. Quality and Reliability Engineering International Published by John Wiley & Sons Ltd.     

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.     

A Multivariate Control Chart for Expected Changes Over Time

A new procedure is proposed that merges the methodologies of regression control charts and multivariate control charts. The simulation of this procedure shows that this new control chart can be very effective in detecting even modestly larger than expected changes in several monitored variables which are subject to some naturally occurring changes over time.     

Alternatives to the Multivariate Control Chart for Process Dispersion

In this article, we compare the performances of six new multivariate control chart schemes for process dispersion to the standard multivariate process dispersion control chart. The six new schemes are designed by transforming the standard multivariate control chart statistic for process dispersion into a standard scale so that runs rules can be incorporated into these schemes. This article discusses a simple extension for using runs rules in a multivariate control chart for process dispersion. The extension is deemed important since the use of runs rules is always confined to univariate control charts only. The performances of the six control chart schemes together with the standard control chart are based on the computed average run length (ARL) profiles. Five of the six schemes have shown better ARL performances than the standard multivariate process dispersion control chart.