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A synthetic mean square error (MSE) control chart is presented in this study for monitoring the changes in the mean and standard deviation of a normally distributed process. The synthetic MSE control chart is a combination of the standard MSE control chart and the conforming run length (CRL) control chart. From the numerical comparisons, the synthetic MSE control chart is always more efficient than the standard MSE control chart in detecting shifts in the process mean and standard deviation. The synthetic MSE chart also performs better than the exponentially weighted moving average-semicircle (EWMA-SC) chart, except for some cases where the process mean shifts are small. [ABSTRACT FROM PUBLISHER]

Economic and economic-statistical models are developed for the syntheticT2chart. The input parameters that result in larger cost and affect the optimal parameters are identified. The optimal parameters are quite robust toward changes in input parameters, except the number of variables and the Mahalanobis distance. Alternative choices of parameters, which result in minimal cost increase, can be chosen if it is infeasible to operate the chart optimally. The results are based on numerical examples and verified through simulation. The syntheticT2chart has better economic and economic-statistical performances than the Hotelling'sT2and MEWMA charts under most conditions. [ABSTRACT FROM PUBLISHER]

Rims rules are used to increase the sensitivity of the Shewhart &Xmacr; control chart in detecting small and moderate process mean shifts. Most of the &Xmacr; charts incorporating runs rules are designed based on the average run length (ARL). It is known that the shape of the run length distribution changes according to the magnitude of the shift in the process mean, ranging from highly skewed when the process is in-control to appro&Xmacr;imately symmetric when the shift is large. Since the shape of the run length distribution changes with the magnitude of the shift in the mean, the median run length (MRL) provides a more meaningful e&Xmacr;planation about the in-control and out-of-control performances of a control chart. In this article, we propose the design of the revised m-of-k runs rule based on MRL. In addition, the standard deviation of the run length (SDRL) of the revised m-of-k rule will also be studied. The revised m-of-k runs rule, suggested by Antzoulakos and Rakitzis (2008), was originally designed based on ARL. The Markov chain technique is employed to obtain the MRLs. Compared with the standard &Xmacr; chart, the MRL results show that the revised rules give better performances for small and moderate mean shifts, while maintaining the same sensitivity towards large mean shifts. The MRL results are in accordance with the results obtained by Antzoulakos and Rakitzis (2008), where the rules are designed based on ARL. [ABSTRACT FROM AUTHOR]

Control charts are usually designed using average run length as the criterion to be optimized. The shape of the run length distribution changes according to the shift in the mean, from highly skewed for an in-control process to approximately symmetric when the mean shift is large. Since the shape of the run length distribution changes with the mean shift, the Median Run Length (MRL) provides a more meaningful interpretation for in-control and out-of-control performances of the charts, and it is readily understood by practitioners. This article presents an optimal design procedure for a synthetic chart able to monitor the mean based on the MRL under the zero- and steady-state modes. The synthetic chart integrates and conforming run length charts. Pseudocodes and Mathematica programs are presented for the computation of the optimal parameters of the synthetic chart based on a desired in-control MRL (MRL(0)), a given sample size, and a specified mean shift for which a quick detection is needed. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for additional example, additional performance study, proof, tables, and figures.] [ABSTRACT FROM PUBLISHER]

Two generally weighted moving average (GWMA) charts are usually used concurrently for a simultaneous monitoring of the process mean and process variance. In this article, we propose a new GWMA chart, called the Max-GWMA chart, which uses a single statistic for a simultaneous monitoring of the process mean and variance. The statistic of the Max-GWMA chart is based on the maximum of the absolute values of two GWMA statistics, one for controlling the mean while the other the variance. We show that the Max-GWMA chart outperforms the combined GWMA chart, in terms of the average run length (ARL), standard deviation of the run length (SDRL) and diagnostic abilities performances. The combined GWMA chart consists of two GWMA charts that are run concurrently, one for monitoring the mean and the other the variance. [ABSTRACT FROM AUTHOR]

In this article, we extend the single Max-EWMA chart to a single double EWMA chart, called the Max-DEWMA chart. The statistics of the Max-DEWMA chart are based on the maximum of the absolute values of the two DEWMA statistics, one controlling the mean while the other the variance. We show that the Max-DEWMA chart performs better than the Max-EWMA chart in detecting small and moderate shifts in the mean and/or variance. [ABSTRACT FROM AUTHOR]

In this article, a synthetic scaled weighted variance X… (synthetic SWV-X…) control chart is proposed to monitor the process mean of skewed populations. This control chart is an improvement over the synthetic weighted variance X… (synthetic WV-X…) chart suggested by Khoo et al. (2008), in the detection of a negative shift in the mean. A comparison between the performances of the synthetic SWV-X… and synthetic WV-X… charts are made in terms of the average run length (ARL) values for the various levels of skewnesses as well as different magnitudes of positive and negative shifts in the mean. A method to construct the synthetic SWV-X… chart is explained in detail. An illustrative example is also given to show the implementation of the synthetic SWV-X… chart. [ABSTRACT FROM AUTHOR]

This article proposes a multivariate synthetic control chart for skewed populations based on the weighted standard deviation method. The proposed chart incorporates the weighted standard deviation method into the standard multivariate synthetic control chart. The standard multivariate synthetic chart consists of the Hotelling's T2 chart and the conforming run length chart. The weighted standard deviation method adjusts the variance-covariance matrix of the quality characteristics and approximates the probability density function using several multivariate normal distributions. The proposed chart reduces to the standard multivariate synthetic chart when the underlying distribution is symmetric. In general, the simulation results show that the proposed chart performs better than the existing multivariate charts for skewed populations and the standard T2 chart, in terms of false alarm rates as well as moderate and large mean shift detection rates based on the various degrees of skewnesses. [ABSTRACT FROM AUTHOR]

The double exponentially weighted moving average (DEWMA) technique has been investigated in recent years for detecting shifts in the process mean and has been shown to be more efficient than the corresponding exponentially weighted moving average (EWMA) technique. In this article, we extend the DEWMA technique of performing exponential smoothing twice to the double moving average (DMA) technique by computing the moving average twice. Using simulation, we show that our proposed DMA chart improves upon the ARL performance of the moving average (MA) chart in detecting mean shifts of small to moderate magnitudes. It is also shown through simulation that, generally, the DMA charts with spans, w = 10 and 15 provide comparable average run length (ARL) performances to the EWMA and cumulative sum (CUSUM) charts, designed for detecting small shifts. [ABSTRACT FROM AUTHOR]

Statistical design is applied to a multivariate exponentially weighted moving average (MEWMA) control chart. The chart parameters are control limit H and smoothing constant r . The choices of the parameters depend on the number of variables p and the size of the process mean shift δ. The MEWMA statistic is modeled as a Markov chain and the Markov chain approach is used to determine the properties of the chart. Although average run length has become a traditional measure of the performance of control schemes, some authors have suggested other measures, such as median and other percentiles of the run length distribution to explain run length properties of a control scheme. This will allow a thorough study of the performance of the control scheme. Consequently, conclusions based on these measures would provide a better and comprehensive understanding of a scheme. In this article, we present the performance of the MEWMA control chart as measured by the average run length and median run length. Graphs are given so that the chart parameters of an optimal MEWMA chart can be determined easily. [ABSTRACT FROM AUTHOR]

Runs rules are incorporated into the Shewhart X control chart to increase its sensitivity in detecting small process shifts so that assignable causes can be detected more quickly. In this article, two improved runs rules are suggested. Average run length values for these new improved rules are computed and compared with that of the existing ones. The comparison shows that the new improved rules are superior in performance for large process average shifts, while maintaining the same sensitivity in the detection of small shifts. [ABSTRACT FROM AUTHOR]

The monitoring of the variance of a process is important because it provides information about process improvement and deterioration. A process improvement is indicated by a reduction in the variance, whereas a process deterioration is shown by an increment in the variance. The R and S charts are widely used in the monitoring of the process variance for subgrouped data. In cases where the production rate is slow and monitoring of the process is required before the time needed to form a subgroup, control charting procedures based on individual measurements have been developed. This article discusses an approach to identify the exact time of a permanent shift in the process variance as a result of process improvement or deterioration using the maximum likelihood estimation techniques. [ABSTRACT FROM AUTHOR]

Both the R and S charts are widely used in many manufacturing industries to monitor the process dispersion. The R chart is more popular among quality control practitioners especially when dealing with small sample sizes because of the simplicity of computing the range, R , from each sample. For larger sample sizes, the preferred choice is the S chart because it is slightly more effective than the R chart. The computation of the standard deviation, S , from each sample can now be made easily due to the availability of computers and scientific calculators. This article addresses the shortcomings of the conventional S chart and suggests a modified S chart to overcome these problems. [ABSTRACT FROM AUTHOR]

A semicircle control chart can be used in detecting both increases and decreases in the mean and/or variance. In this paper, we propose two modified semicircle charts for detecting a reduction in the process variance, a.k.a. process improvement. Each of these modified semicircle charts, namely, SC1 and SC2 has two limits, defined by the inner and outer semicircles. A process improvement is detected by the SC1 scheme if a point is plotted inside the smallest semicircle, or if two successive points are plotted between the inner and outer semicircles and by the SC2 scheme if a point plots inside the smallest semicircle or if two of three successive points plot between the inner and outer semicircles. It will be shown that the two modified semicircle charts have superior average run length (ARL) performances to the basic semicircle chart in the detection of process improvement. The ARL study is conducted by means of a simulation. [ABSTRACT FROM AUTHOR]

The monitoring of the process average is usually done with the control chart for the means (a.k.a. the X chart). However, the sample average, X , is sensitive to outliers which are observations whose values are larger or smaller than the majority of the other observations. The median statistic, on the other hand, is robust to outliers. The occurrence of outliers could be due to either the presence of assignable causes or common causes. Suppose that from past experiences, the occurrence of outliers in a certain process which happen occasionally is usually associated with the presence of common causes and that assignable causes will lead to permanent shifts in the process. Under such situations, using a median chart is more suitable because the chart's limits are less influenced by outliers so that unnecessary revision of the limits can be avoided. For these situations, occasional outliers (due to common causes) occurring in a subgroup will lead to an underestimated or overestimated sample average, hence producing more frequent false out-of-control signals for the X chart. If our major concern is the detection of assignable causes which lead to permanent shifts in the process and not occasional outliers that cause temporary shifts, the use of a sample median chart is justified. Another reason which justifies the use of a sample median chart is because it is an easy to plot chart, especially for odd sample sizes. [ABSTRACT FROM AUTHOR]

This paper discusses an easy approach for increasing the sensitivity of the p chart by incorporating runs rules. A method for calculating the exact control limits for the various standardized p chart schemes incorporating runs rules is shown. Simple mathematical calculations reveal that the performances of all p chart schemes incorporating runs rules are superior to that of the standard approach. These calculations enable practitioners to determine the average run length (ARL) value that corresponds to a certain level of fraction nonconforming, p1, based on a standard or known predefined proportion of nonconforming items, p0. Examples are given to illustrate the application of the procedures discussed. [ABSTRACT FROM AUTHOR]

Runs rules are often used to increase the sensitivity of a Shewhart control chart. In this work, plots of various runs rules schemes are given to simplify the determination of control limits based on a desired in-control average run length (ARL0). [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we will discuss a simple way for monitoring shifts in the covariance matrix of a p-dimensional multivariate normal process distribution, Np(μ,Σ). An exact method based on the chi-square distribution for constructing multivariate control limits will also be shown. We will illustrate the proposed procedure at work based on an example. [ABSTRACT FROM AUTHOR]

This paper illustrates a simple and effective method of incorporating runs rules into Hotelling χ2 control charts. A Markov chain will be used to obtain a desired in-control average run length (ARL). Comparisons between the basic multivariate χ2 control chart and the multivariate χ2 control chart, which incorporates the various runs rules, are based on their respective ARL performances. All multivariate χ2 control charts that incorporate the various runs rules have shown better ARL performance compared to the basic multivariate χ2 control chart for small shifts in distance λ from the in-control mean vector μ0 to the out-of-control mean vector μs. An example of the application, based on the proposed method, is also given. [ABSTRACT FROM AUTHOR]

Multivariate CUSUM control charts are often used instead of the standard Hotelling's control charts in many practical problems when detection of small shifts in the process mean is important. However, design of multivariate CUSUM control charts are usually based on the average run length (ARL). In this work, we will compute the percentage points of the run-length distributions of two multivariate CUSUM control charts. It will be shown that interpretations based on ARL can be misleading since the in-control run-length distribution of a multivariate CUSUM is highly skewed. On the other hand, the percentage points of the run-length distribution provide additional information such as the median run length, early false out-of-control signals, and the skewness of the run-length distribution for a particular scheme. These extra information might provide quality control engineers further knowledge of a particular multivariate CUSUM control chart scheme. [ABSTRACT FROM AUTHOR]

In recent years, there is a trend in manufacturing industries to produce smaller lot sizes or low volume production. This trend is due to increased emphasis on just-in-time techniques (JIT), synchronous manufacturing, job-shop settings, the reduction of in-process inventory, and costs. The term used to describe such low volume production is “Short Runs Production” or more commonly “Short Runs.” In such an environment, the run of a process is short, usually fewer than 50. Therefore, a principal practical problem is the need to chart a large number of different processes and the consequent large number of charts required. This article discusses proposed multivariate control charts for short runs based on individual measurements and subgrouped data. [ABSTRACT FROM AUTHOR]