Multivariate process dispersion monitoring without subgrouping

The memory-type adaptive and non-adaptive control charts are among the best control charts for detecting small-to-moderate changes in the process parameter(s). In this paper, we propose the Crosier CUSUM (CCUSUM), EWMA, adaptive CCUSUM (ACCUSUM) and adaptive EWMA (AEWMA) charts for efficiently monitoring the changes in the covariance matrix of a multivariate normal process without subgrouping. Using extensive Monte Carlo simulations, the length characteristics of these control charts are computed. It turns out that the ACCUSUM and AEWMA charts perform uniformly and substantially better than the CCUSUM and EWMA charts when detecting a range of shift sizes in the covariance matrix. Moreover, the AEWMA chart outperforms the ACCUSUM chart. A real dataset is used to explain the implementation of the proposed control charts.     

Statistical surveillance of the mean vector and the covariance matrix of nonlinear time series

The purpose of this paper is to jointly monitor the mean vector and the covariance matrix of multivariate nonlinear times series. The underlying target process is assumed to be a constant conditional correlation process Bollerslev (Rev Econ Stat 72:498–505, 1990) or a dynamic conditional correlation model Engle (J Bus Econ Stat 20:339–350, 2002). We introduce several EWMA and CUSUM control charts. These control schemes are based on univariate EWMA statistics, multivariate EWMA recursions, and different types of cumulative sums. The recursions are applied to local measures for means and covariances, e.g. the present observations and the conditional covariances. Further, they are applied to means and covariances of residuals. The control statistics are obtained by computing the Mahalanobis distance between the EWMA or CUSUM statistics and their expectations if no change occurs. Via Monte Carlo simulation the performance of the proposed charts is compared. Our empirical study illustrates an application of these control procedures to bivariate logarithmic returns of the European indices FTSE100 and DAX. In order to assess the performance of the introduced schemes we apply the average run length and the maximum conditional expected delay.     

An Empirical-Likelihood-Based Multivariate EWMA Control Scheme

Nonparametric control charts are useful in statistical process control (SPC) when there is a lack of or limited knowledge about the underlying process distribution, especially when the process measurement is multivariate. This article develops a new multivariate SPC methodology for monitoring location parameter based on adapting a well-known nonparametric method, empirical likelihood (EL), to on-line sequential monitoring. The weighted version of EL ratio test is used to formulate the charting statistic by incorporating the exponentially weighted moving average control (EWMA) scheme, which results in a nonparametric counterpart of the classical multivariate EWMA (MEWMA). Some theoretical and numerical studies show that benefiting from using EL, the proposed chart possesses some favorable features. First, it is a data-driven scheme and thus is more robust to various multivariate non-normal data than the MEWMA chart under the in-control (IC) situation. Second, it is transformation-invariant and avoids the estimation of covariance matrix from the historical data by studentizing internally, and hence its IC performance is less deteriorated when the number of reference sample is small. Third, in comparison with the existing approaches, it is more efficient in detecting small and moderate shifts for multivariate non-normal process.     

Effect of measurement error on exponentially weighted moving average control charts under ranked set sampling schemes

Control charts are a powerful statistical process monitoring tool often used to monitor the stability of manufacturing processes. In quality control applications, measurement errors adversely affect the performance of control charts. In this paper, we study the effect of measurement error on the detection abilities of the exponentially weighted moving average (EWMA) control charts for monitoring process mean based on ranked set sampling (RSS), median RSS (MRSS), imperfect RSS (IRSS) and imperfect MRSS (IMRSS) schemes. We also study the effect of multiple measurements and non-constant error variance on the performances of the EWMA control charts. The EWMA control chart based on simple random sampling is compared with the EWMA control charts based on RSS, MRSS, IRSS and IMRSS schemes. The performances of the EWMA control charts are evaluated in terms of out-of-control average run length and standard deviation of run lengths. It turns out that the EWMA control charts based on MRSS and IMRSS schemes are better than their counterparts for all measurement error cases considered here.     

An Improved Distribution-free EWMA Mean Chart

Control charts are effective tools for signal detection in both manufacturing processes and service processes. Much service data come from a process with variables having nonnormal or unknown distributions. The commonly used Shewhart variable control charts, which depend heavily on the normality assumption, should not be properly used here. In this article, we propose an improved asymmetric EWMA mean chart based on a simple statistic to monitor process mean shift. We explored the sampling properties of the new monitoring statistic and calculated the average run lengths of the proposed asymmetric EWMA mean chart. We recommend the proposed improved asymmetric EWMA mean chart because the average run lengths of the modified charts are more accurate and reasonable than those of the five existed mean charts. A numerical example of service times with a right skewed distribution from a service system of a bank branch is used to illustrate the application of the improved asymmetric EWMA mean chart and to compare it with the five existing mean charts. The proposed chart showed better detection performance than those of the five existing mean charts in monitoring and detecting shifts in the process mean.     

Sequential monitoring of minimum variance portfolio

This paper evaluates the economic effect of monitoring the minimum variance portfolio weights, which depend solely on the covariance matrix of returns. The investor decides whether the portfolio composition providing the smallest portfolio variance remains optimal at the beginning of every new investment period. For this purpose changes in the optimal weights are sequentially detected by means of EWMA control charts. Signals obtained from monitoring are used for improvement of the covariance matrix estimation procedure. The investment strategy exploiting signals from control charts is compared with a number of alternative approaches in the empirical study.     

Grouped data exponentially weighted moving average control charts

In the manufacture of metal fasteners in a progressive die operation, and other industrial situations, important quality dimensions cannot be measured on a continuous scale, and manufactured parts are classified into groups by using a step gauge. This paper proposes a version of exponentially weighted moving average (EWMA) control charts that are applicable to monitoring the grouped data for process shifts. The run length properties of this new grouped data EWMA chart are compared with similar results previously obtained for EWMA charts for variables data and with those for cumulative sum (CUSUM) schemes based on grouped data. Grouped data EWMA charts are shown to be nearly as efficient as variables-based EWMA charts and are thus an attractive alternative when the collection of variables data is not feasible. In addition, grouped data EWMA charts are less affected by the discreteness that is inherent in grouped data than are grouped data CUSUM charts. In the metal fasteners application, grouped data EWMA charts were simple to implement and allowed the rapid detection of undesirable process shifts.     

A new nonparametric synthetic EWMA control chart for monitoring process mean

The exponentially weighted moving average (EWMA) control charts are widely used in chemical and process industries because of their excellent speed in catching small to moderate shifts in the process target. In usual practice, many data come from a process where the monitoring statistic is non-normally distributed or it follows an unknown probability distribution. This necessitates the use of distribution-free/nonparametric control charts for monitoring the deviations from the process target. In this paper, we integrate the existing EWMA sign chart with the conforming run length chart to propose a new synthetic EWMA (SynEWMA) sign chart for monitoring the process mean. The SynEWMA sign chart encompasses the synthetic sign and EWMA sign charts. Monte Carlo simulations are used to compute the run length profiles of the SynEWMA sign chart. Based on a comprehensive comparison, it turns out that the SynEWMA sign chart is able to perform substantially better than the existing EWMA sign chart. Both real and simulated data sets are used to explain the working and implementation of existing and proposed control charts.     

A new approach for monitoring process variance

ABSTRACT

Control charts are effective tools for signal detection in both manufacturing processes and service processes. Much service data come from a process with variables having non-normal or unknown distributions. The commonly used Shewhart variable control charts, which depend heavily on the normality assumption, should not be properly used in such circumstances. In this paper, we propose a new variance chart based on a simple statistic to monitor process variance shifts. We explore the sampling properties of the new monitoring statistic and calculate the average run lengths (ARLs) of the proposed variance chart. Furthermore, an arcsine transformed exponentially weighted moving average (EWMA) chart is proposed because the ARLs of this modified chart are more intuitive and reasonable than those of the variance chart. We compare the out-of-control variance detection performance of the proposed variance chart with that of the non-parametric Mood variance (NP-M) chart with runs rules, developed by Zombade and Ghute [Nonparametric control chart for variability using runs rules. Experiment. 2014;24(4):1683–1691], and the nonparametric likelihood ratio-based distribution-free exponential weighted moving average (NLE) chart and the combination of traditional exponential weighted moving average (EWMA) mean and EWMA variance (CEW) control chart proposed by Zou and Tsung [Likelihood ratio-based distribution-free EWMA control charts. J Qual Technol. 2010;42(2):174–196] by considering cases in which the critical quality characteristic has a normal, a double exponential or a uniform distribution. Comparison results showed that the proposed chart performs better than the NP-M with runs rules, and the NLE and CEW control charts. A numerical example of service times with a right-skewed distribution from a service system of a bank branch in Taiwan is used to illustrate the application of the proposed variance chart and of the arcsine transformed EWMA chart and to compare them with three existing variance (or standard deviation) charts. The proposed charts show better detection performance than those three existing variance charts in monitoring and detecting shifts in the process variance.     

An EWMA chart for monitoring process mean

In the statistical process control literature, there exists several improved quality control charts based on cost-effective sampling schemes, including the ranked set sampling (RSS) and median RSS (MRSS). A generalized cost-effective RSS scheme has been recently introduced for efficiently estimating the population mean, namely varied L RSS (VLRSS). In this article, we propose a new exponentially weighted moving average (EWMA) control chart for monitoring the process mean using VLRSS, named the EWMA-VLRSS chart, under both perfect and imperfect rankings. The EWMA-VLRSS chart encompasses the existing EWMA charts based on RSS and MRSS (named the EWMA-RSS and EWMA-MRSS charts). We use extensive Monte Carlo simulations to compute the run length characteristics of the EWMA-VLRSS chart. The proposed chart is then compared with the existing EWMA charts. It is found that, with either perfect or imperfect rankings, the EWMA-VLRSS chart is more sensitive than the EWMA-RSS and EWMA-MRSS charts in detecting small to large shifts in the process mean. A real dataset is also used to explain the working of the EWMA-VLRSS chart.     

A mixed GWMA–CUSUM control chart for monitoring the process mean

The memory-type control charts are widely used in the process and service industries for monitoring the production processes. The reason is their sensitivity to quickly react against the small process disturbances. Recently, a new cumulative sum (CUSUM) chart has been proposed that uses the exponentially weighted moving average (EWMA) statistic, called the EWMA–CUSUM chart. Similarly, in order to further enhance the sensitivity of the EWMA–CUSUM chart, we propose a new CUSUM chart using the generally weighted moving average (GWMA) statistic, called the GWMA–CUSUM chart, for efficiently monitoring the process mean. The GWMA–CUSUM chart encompasses the existing CUSUM and EWMA–CUSUM charts. Extensive Monte Carlo simulations are used to explore the run length profiles of the GWMA–CUSUM chart. Based on comprehensive run length comparisons, it turns out that the GWMA–CUSUM chart performs substantially better than the CUSUM, EWMA, GWMA, and EWMA–CUSUM charts when detecting small shifts in the process mean. An illustrative example is also presented to explain the implementation and working of the EWMA–CUSUM and GWMA–CUSUM charts.     

Multivariate control charts based on a projection approach

Summary: In this paper the projection approach of Runger (1996) is applied to construct control charts for a multivariate process. It is assumed that a shift in the mean might only occur in a known subspace of the parameter space. The projection method permits a reduction of the dimensionality of the control problem.Several control schemes based on projections are introduced. We consider CUSUM type charts as well as EWMA schemes. The underlying variables are assumed to be independent and normally distributed. Using the average run length all control charts are compared with each other. Moreover, it is analyzed how sensitive the charts react on a false choice of the subspace.     

A new adaptive EWMA control chart using auxiliary information for monitoring the process mean

The adaptive memory-type control charts, including the adaptive exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) charts, have gained considerable attention because of their excellent speed in providing overall good detection over a range of mean shift sizes. In this paper, we propose a new adaptive EWMA (AEWMA) chart using the auxiliary information for efficiently monitoring the infrequent changes in the process mean. The idea is to first estimate the unknown process mean shift using an auxiliary information based mean estimator, and then adaptively update the smoothing constant of the EWMA chart. Using extensive Monte Carlo simulations, the run length profiles of the AEWMA chart are computed and explored. The AEWMA chart is compared with the existing control charts, including the classical EWMA, CUSUM, synthetic EWMA and synthetic CUSUM charts, in terms of the run length characteristics. It turns out that the AEWMA chart performs uniformly better than these control charts when detecting a range of mean shift sizes. An illustrative example is also presented to demonstrate the working and implementation of the proposed and existing control charts.     

A New Adaptive Variable Sample Size Approach in EWMA Control Chart

Adaptive control charts have been developed for improving the capability of control charts in detecting small shifts. In this article, we propose a new exponential weighted moving average control chart with variable sample size, in which the sample size is determined as an integer linear function by EWMA statistic value. The performance of the proposed VSS EWMA control chart is compared with FSS EWMA as well as traditional VSS EWMA control charts. The results show the better performance of the proposed VSS strategy respect to the traditional one and fixed sample size.     

Monitoring Process Mean and Variability with One Non-central Chi-square Chart

Traditionally, an X-chart is used to control the process mean and an R-chart to control the process variance. However, these charts are not sensitive to small changes in process parameters. A good alternative to these charts is the exponentially weighted moving average (EWMA) control chart for controlling the process mean and variability, which is very effective in detecting small process disturbances. In this paper, we propose a single chart that is based on the non-central chi-square statistic, which is more effective than the joint X and R charts in detecting assignable cause(s) that change the process mean and/or increase variability. It is also shown that the EWMA control chart based on a non-central chi-square statistic is more effective in detecting both increases and decreases in mean and/or variability.     

Generally weighted moving average control charts using repetitive sampling

Abstract

Generally weighted moving average (GWMA) control charts have been validated for effective detection of small process shifts, and perform better than exponentially weighted moving average (EWMA) control charts. These charts are available based on single sampling; however, repetitive sampling charts have received less attention. Here, a GWMA control chart based on repetitive sampling (namely an RS-GWMA chart) is proposed for enhancing detectability of small process shifts. Simulations show that the proposed RS-GWMA chart with large design and small adjustment parameters outperforms existing hybrid EWMA (HEWMA) control charts based on repetitive sampling. An in-silico example is considered for demonstrating the applicability of the proposed RS-GWMA chart.     

Monitoring simple linear profiles using variable sample size schemes

ABSTRACT

Profile monitoring is one of the new research areas in statistical process control. Most of the control charts in this area are designed with fixed sampling rate which makes the control chart slow in detecting small to moderate shifts. In order to improve the performance of the conventional fixed control charts, adaptive features are proposed in which, one or more design parameters vary during the process. In this paper the variable sample size feature of EWMA₃ and MEWMA schemes are proposed for monitoring simple linear profiles. The EWMA₃ method is based on the combination of three exponentially weighted moving average (EWMA) charts for monitoring three parameters of a simple linear profile separately and the Multivariate EWMA (MEWMA) chart is based on the using a single chart to monitor the coefficients and variance of a general linear profile. Also a two-sided control chart is proposed for monitoring the standard deviation in the EWMA₃ method. The performance of the proposed charts is compared in terms of the average time to signal. Numerical examples show that using adaptive features increase the power of control charts in detecting the parameter shifts. Finally, the performance of the proposed variable sample size schemes is illustrated through a real case in the leather industry.     

On increasing the sensitivity of mixed EWMA–CUSUM control charts for location parameter

Control chart is an important statistical technique that is used to monitor the quality of a process. Shewhart control charts are used to detect larger disturbances in the process parameters, whereas cumulative sum (CUSUM) and exponential weighted moving average (EWMA) are meant for smaller and moderate changes. In this study, we enhanced mixed EWMA–CUSUM control charts with varying fast initial response (FIR) features and also with a runs rule of two out of three successive points that fall above the upper control limit. We investigate their run-length properties. The proposed control charting schemes are compared with the existing counterparts including classical CUSUM, classical EWMA, FIR CUSUM, FIR EWMA, mixed EWMA–CUSUM, 2/3 modified EWMA, and 2/3 CUSUM control charting schemes. A case study is presented for practical considerations using a real data set.     

An exponentially weighted moving average chart controlling false discovery rate

A new control chart is developed by using the exponentially weighted moving average (EWMA) statistics and a multiple testing procedure for controlling false discovery rate. The multiple testing procedure considers not only the current EWMA statistic, but also a given number of previous statistics at the same time. Numerical simulations are accomplished to evaluate the performance of the proposed control chart in terms of the average run length and the conditional expected delay. The results are compared with those of the existing control charts including the X-bar chart, EWMA, and cumulative sum control charts. Case studies with real data-sets are also presented.     

Robustness to non-normality and autocorrelation of individuals control charts

This paper studies the effects of non-normality and autocorrelation on the performances of various individuals control charts for monitoring the process mean and/or variance. The traditional Shewhart X chart and moving range (MR) chart are investigated as well as several types of exponentially weighted moving average (EWMA) charts and combinations of control charts involving these EWMA charts. It is shown that the combination of the X and MR charts will not detect small and moderate parameter shifts as fast as combinations involving the EWMA charts, and that the performana of the X and MR charts is very sensitive to the normality assumption. It is also shown that certain combinations of EWMA charts can be designed to be robust to non-normality and very effective at detecting small and moderate shifts in the process mean and/or variance. Although autocorrelation can have a significant effect on the in-control performances of these combinations of EWMA charts, their relative out-of-control performances under independence are generally maintained for low to moderate levels of autocorrelation.