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.     

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 process mean using generally weighted moving average chart for exponentially distributed characteristics

In this article, we will present a control chart using normal transformation and generally weighted moving average (GWMA) statistic when the quality characteristic follows the exponential distribution. We will develop the necessary measures to monitor the mean of the process using GWMA statistic and analyze the performance using simulation. The average run lengths for monitoring process average are given for various process shifts. The performance of the proposed chart is examined and compared with the existing control chart. The proposed control chart is effective for the monitoring of small shifts in the mean process. The application of the proposed chart is illustrated with the help of simulated data.     

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.     

Applying fast initial response features on GWMA control charts for monitoring autocorrelation data

ABSTRACT

A generally weighted moving average (GWMA) control chart with fast initial response (FIR) features is addressed to monitor an autoregressive process mean shift. Numerical simulations based on average run length (ARL) show that the GWMA control chart with additional FIR feature requires less time to detect small or moderate shifts than GWMA control chart at low level of autocorrelation; whereas these two control charts perform similarly at high level of autocorrelation. Regardless of any level of autocorrelation, GWMA control charts provided with additional FIR feature have a good performance in detecting large shifts during the initial stage.     

The extended GWMA control chart

This study extends the generally weighted moving average (GWMA) control chart by imitating the double exponentially weighted moving average (DEWMA) technique. The proposed chart is called the double generally weighted moving average (DGWMA) control chart. Simulation is employed to evaluate the average run length characteristics of the GWMA, DEWMA and DGWMA control charts. An extensive comparison of these control charts reveals that the DGWMA control chart with time-varying control limits is more sensitive than the GWMA and the DEWMA control charts for detecting medium shifts in the mean of a process when the shifts are between 0.5 and 1.5 standard deviations. Additionally, the GWMA control chart performs better when the mean shifts are below the 0.5 standard deviation, and the DEWMA control performs better when the mean shifts are above the 1.5 standard deviation. The design of the DGWMA control chart is also discussed.     

Generally weighted moving average control charts with fast initial response features

The generally weighted moving average (GWMA) control chart is an extension model of exponentially weighted moving average (EWMA) control chart. Recently, some approaches have been proposed to modify EWMA charts with fast initial response (FIR) features. We introduce these approaches in GWMA-type charts. Via simulation, various control schemes are designed and then their average run lengths are computed and compared. Based on the overall performance, it is showed that the DGWMA chart is the best choice especially when the shift is moderate, and the GWMA charts provided with additional FIR feature have a good performance only in detecting large shifts during the initial stage.     

Ewma control chart under linear drift

An accurate numerical procedure is presented for computing the average run length (ARL) of an exponentially weighted moving average (EWMA) chart under a linear drift in the process mean. The performance of an EWMA chart is then evaluated under a linear drift in the mean. In processes where gradual linear drifts rather than abrupt changes in the mean model the shifts in the mean more accurately, an evaluation of the performance of an EWMA chart under a linear drift is more appropriate. Tables of optimal smoothing parameters and control chart limits are given which make the design of EWMA charts easy.     

The Generally Weighted Moving Average Variance Chart

This article extends the generally weighted moving average (GWMA) technique for detecting changes in process variance. The proposed chart is called the generally weighted moving average variance (GWMAV) chart. Simulation is employed to evaluate the average run length (ARL) characteristics of the GWMAV and EWMA control charts. An extensive comparison of these control charts reveals that the GWMAV chart is more sensitive than the EWMA control charts for detecting small shifts in the variance of a process when the shifts are below 1.35 standard deviations. Additionally, the GWMAV control chart performs little better when the variance shifts are between 1.35 and 1.5 standard deviation, and the 2 charts performs similar when the variance shifts are above 1.5 standard deviation. The design of the GWMAV chart is also discussed.     

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.     

Non parametric double generally weighted moving average sign charts based on process proportion

Non parametric control charts have received increasing attention in the field of statistical process control. This paper presents a non parametric double generally weighted moving average (DGWMA) sign chart for monitoring small deviations when the quality characteristics of a process are unknown. The statistical performance of the non parametric DGWMA sign chart is evaluated and compared with those of other charts, including the exponentially weighted moving average (EWMA), generally weighted moving average (GWMA), and double EWMA (DEWMA) sign charts. Simulation studies indicate that the non parametric DGWMA sign chart with a large design and median adjustment parameters is always more sensitive than other charts in detecting small changes.     

A weighted likelihood ratio test-based chart for monitoring process mean and variability

In this paper, a new single exponentially weighted moving average (EWMA) control chart based on the weighted likelihood ratio test, referred to as the WLRT chart, is proposed for the problem of monitoring the mean and variance of a normally distributed process variable. It is easy to design, fast to compute, and quite effective for diverse cases including the detection of the decrease in variability and individual observation case. The optimal parameters that can be used as a design aid in selecting specific parameter values based on the average run length (ARL) and the sample size are provided. The in-control (IC) and out-of-control (OC) performance properties of the new chart are compared with some other existing EWMA-type charts. Our simulation results show that the IC run length distribution of the proposed chart is similar to that of a geometric distribution, and it provides quite a robust and satisfactory overall performance for detecting a wide range of shifts in the process mean and/or variability.     

Statistical control charts for monitoring the mean of a stationary process

Recently statistical process control (SPC) methodologies have been developed to accommodate autocorrelated data. A primary method to deal with autocorrelated data is the use of residual charts. Although this methodology has the advantage that it can be applied to any autocorrelated data it needs time series modeling efforts. In addition for a X residual chart the detection capability is sometimes small compared to the X chart and EWMA chart. Zhang (1998) proposed the EWMAST chart which is constructed by charting the EWMA statistic for stationary processes to monitor the process mean. The performance of the EWMAST chart the X chart the X residual chart and other charts were compared in Zhang (1998). In this paper comparisons are made among the EWMAST chart the CUSUM residual chart and EWMA residual chart as well as the X residual chart and X chart via the average run length.     

Evaluation of control charts under linear trend

The performance of several control charting schemes is studied when the process mean changes as a linear trend. The control charts considered include the Shewhart chart, the Shewhart chart supplemented with runs rules, the cumulative sum (CUSUM) chart, the exponentially weighted moving average (EWMA) chart, and a generalized control chart.     

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.     

Fast Initial Response Features for Poisson GWMA Control Charts

The Poisson GWMA (PGWMA) control chart is an extension model of Poisson EWMA chart. It is substantially sensitive to small process shifts for monitoring Poisson observations. Recently, some approaches have been proposed to modify EWMA charts with fast initial response (FIR) features. In this article, we employ these approaches in PGWMA charts and introduce a novel chart called Poisson double GWMA (PDGWMA) chart for comparison. Using simulation, various control schemes are designed and their average run lengths (ARLs) are computer and compared. It is shown that the PDGWMA chart is the first choice in detecting small shifts especially when the shifts are downward, and the PGWMA chart with adjusted time-varying control limits performs excellently in detecting great process shifts during the initial stage.     

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.     

Poisson GWMA Control Chart

A generally weighted moving average (GWMA) control chart for monitoring Poisson observations is introduced. Using simulation, its average run lengths and standard deviations of run lengths are compared with those of other control charts for Poisson data. It is shown that the Poisson GWMA chart outperforms other control charts, especially when the process shift is small.     

A New GWMA Control Chart for Monitoring Process Mean and Variability

In this article, we extend a single exponentially weighted moving average semicircle (EWMA-SC) chart to a single generally weighted moving average (GWMA) chart. This new control chart can effectively combine the features of the SC chart with GWMA techniques, and can easily indicate the source and direction of a change. We perform simulations to evaluate the average run length, standard deviation of the run length, and diagnostic abilities of the GWMA-SC and EWMA-SC charts. An extensive comparison shows that the GWMA-SC control chart is more sensitive than the EWMA-SC chart for detecting small shifts in the process mean and/or variability.     

Monitoring of autocorrelated general linear profiles

A collection of quality data represented by a functional relationship between response and explanatory variables is called a profile. In the literature, the errors of profiles are often assumed to be independent. However, quality data often exhibits time correlations in real applications. Therefore, in this paper, we investigate a general linear regression model with a between-profile autocorrelation. We propose a multivariate exponentially weighted moving average chart for monitoring shifts in the regression parameters, and an exponentially weighted moving average chart for monitoring shifts in the standard deviation. A simulation study reveals that our proposed schemes outperform competing existing schemes based on the average run length criterion. An example is used to illustrate the applicability of the proposed scheme.