An efficient adaptive EWMA control chart for monitoring the process mean

In recent years, the memory‐type control charts—exponentially weighted moving average (EWMA) and cumulative sum (CUSUM)—along with the adaptive and dual control‐charting structures have received considerable attention because of their excellent ability in providing an overall good detection over a range of mean‐shift sizes. These adaptive memory‐type control charts include the adaptive exponentially weighted moving average (AEWMA), dual CUSUM, and adaptive CUSUM charts. In this paper, we propose a new AEWMA chart for efficiently monitoring the process mean. The idea is to first design an unbiased estimator of the mean shift using the EWMA statistic and then adaptively update the smoothing constant of the EWMA chart. The run length profiles of the proposed AEWMA chart are computed using extensive Monte Carlo simulations. Based on a comprehensive comparative study, it turns out that the proposed AEWMA chart performs better than the existing AEWMA, adaptive CUSUM, dual CUSUM, and Shewhart‐CUSUM charts, in terms of offering more balanced protection against mean shifts of different sizes. An example is also used to explain the working of the existing and proposed control charts.     

Function-based adaptive exponentially weighted moving average dispersion control chart

In this study, a new process dispersion monitoring control chart is proposed based on a function-based adaptation to select the smoothing constant value, named as a function-based adaptive exponentially weighted moving average (EWMA) dispersion control chart. It is suggested to track shift ranges first expected in process dispersion by opting for smoothing constant computation with the help of a function. The shift magnitude assessment is made by an unbiased estimator that determines the smoothing constant value through the proposed function. The enhanced efficiency of the proposed chart can be assessed in terms of smaller run-length profiles, which are determined through Monte Carlo simulations. The proposed chart is compared with the existing adaptive EWMA dispersion chart, and it turned out to perform substantially efficiently in detecting all kinds of decreasing and increasing process dispersion shift magnitudes. Moreover, a real-life dataset application is explained in the example section to elaborate on the ease of implementation in the real-life scenario.     

New EWMA control charts for monitoring process dispersion using auxiliary information

The exponentially weighted moving average (EWMA) control chart is a well‐known statistical process monitoring tool because of its exceptional pace in catching infrequent variations in the process parameter(s). In this paper, we propose new EWMA charts using the auxiliary information for efficiently monitoring the process dispersion, named the auxiliary‐information–based (AIB) EWMA (AIB‐EWMA) charts. These AIB‐EWMA charts are based on the regression estimators that require information on the quality characteristic under study as well as on any related auxiliary characteristic. Extensive Monte Carlo simulation are used to compute and study the run length profiles of the AIB‐EWMA charts. The proposed charts are comprehensively compared with a recent powerful EWMA chart—which has been shown to be better than the existing EWMA charts—and an existing AIB‐Shewhart chart. It turns out that the proposed charts perform uniformly better than the existing charts. An illustrative example is also given to explain the implementation and working of the AIB‐EWMA charts.     

New GWMA‐CUSUM control chart for monitoring the process dispersion

The cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been widely accepted because of their fantastic speed in identifying small‐to‐moderate unusual variations in the process parameter(s). Recently, a new CUSUM chart has been proposed that uses the EWMA statistic, called the CS‐EWMA chart, for monitoring the process variability. On similar lines, in order to further improve the detection ability of the CS‐EWMA chart, we propose a CUSUM chart using the generally weighted moving average (GWMA) statistic, named the GWMA‐CUSUM chart, for monitoring the process dispersion. Monte Carlo simulations are used to compute the run length profiles of the GWMA‐CUSUM chart. On the basis of the run length comparisons, it turns out that the GWMA‐CUSUM chart outperforms the CUSUM and CS‐EWMA charts when identifying small variations in the process variability. A simulated dataset is also used to explain the working and implementation of the CS‐EWMA and GWMA‐CUSUM charts.     

Efficient bivariate EWMA charts for monitoring process dispersion

To ensure high quality standards of a process, the application of control charts to monitor process performance has become a regular routine. Multivariate charts are a preferred choice in the presence of more than one process variable. In this article, we proposed a set of bivariate exponentially weighted moving average (EWMA) charts for monitoring the process dispersion. These charts are formulated based on a variety of dispersion statistics considering normal and non-normal bivariate parent distributions. The performance of the different bivariate EWMA dispersion charts is evaluated and compared using the average run length and extra quadratic loss criteria. For the bivariate normal process, the comparisons revealed that the EWMA chart based on the maximum standard deviation (SMAX_E) was the most efficient chart when the shift occurred in one quality variable. It also performed well when the sample size is small and the shift occurred in both quality variables. The EWMA chart based on the maximum average absolute deviation from median (MDMAX_E) performed better than the other charts in most situations when the shift occurred in the covariance matrix for the bivariate non-normal processes. An illustrative example is also presented to show the working of the charts.     

An adaptive approach to EWMA dispersion chart using Huber and Tukey functions

Random causes are vital part of every process in manufacturing and nonmanufacturing environments, and these do not affect the product features. Special causes, on the other hand, come because of some burden(s) in a process and requires special attention; otherwise, it ruins the products excellence. Special causes are categorized into small, moderate, and large shifts and are handled by statistical quality control charts. The Shewhart control chart is well known for large shifts, while the cumulative sum and exponentially weighted moving average are more effective in detecting small to moderate shifts. However, in practice, many processes require the simultaneous monitoring of both the small to the large shifts. In this study, we have designed an adaptive EWMA for dispersion parameter in connection with Huber and Tukey's bisquare functions. The performance measures used in this study include average run length, extra quadratic loss, relative average run length, and performance‐comparison index. We have observed that the study proposals are good competitors to the other counter parts for an efficient monitoring of shifts of varying amounts. An illustrative example using real data is given to demonstrate the implementation of the study proposal.     

A moving average control chart using a robust scale estimator for process dispersion

Control charts are one of the most powerful tools used to detect and control industrial process deviations in statistical process control. In this paper, a moving average control chart based on a robust scale estimator of standard deviation, namely, the sample median absolute deviation (MAD) statistic, for monitoring process dispersion, is proposed. A simulation study is conducted to evaluate the performance of the proposed moving average median absolute deviation (MA‐MAD) chart, in terms of average run length for various distributions. The results show that the moving average MAD chart performs well in detecting small and moderate shifts in process dispersion, especially when the normality assumption is violated. In addition, this chart is very efficient, especially when the quality characteristic follows a skewed distribution. Numerical and simulated examples are given at the end of the paper.     

A mixed cumulative sum homogeneously weighted moving average control chart for monitoring process mean

The homogeneously weighted moving average (HWMA) control chart is famous to identify small deviations in the process mean. The plotting statistic of the HWMA chart assigns equal weight among the previous samples as compared to the plotting statistic of the exponentially weighted moving average chart. We propose a new HWMA chart that uses the plotting statistic of the cumulative sum chart. The run length performance of the proposed chart is measured in terms of the average, the standard deviation, some percentile points, and compared with some existing counterparts' charts. The comparison shows that the proposed chart performs superior to their existing counterparts. An application based on a real-life dataset is also presented.     

Enhanced EWMA charts for monitoring the process coefficient of variation

The coefficient of variation (CV) is an important quality characteristic when the process variance is a function of the process mean for a production process. In this paper, we develop an auxiliary information–based (AIB) estimator for estimating the squared CV, along with its approximated mean and variance. This estimator is then used to devise new one-sided EWMA charts for monitoring the increases or decreases in the squared CV of a normal process, named the AIB-EWMA CV charts. In addition, the sensitivities of these control charts are also enhanced with the fast initial response feature. The Monte Carlo simulation method is used to compute the run length characteristics of the proposed CV charts. Based on detailed run length comparisons, it is found that the proposed AIB-EWMA CV charts are uniformly and substantially better than the existing EWMA CV charts when detecting different kinds of upward/downward shifts in the squared CV. The proposed charts are also applied to a real dataset to support the proposed theory.     

A nonparametric CUSUM chart for process dispersion

In the present article, we propose a nonparametric cumulative sum control chart for process dispersion based on the sign statistic using in‐control deciles. The chart can be viewed as modified control chart due to Amin et al, 6 which is based on in‐control quartiles. An average run length performance of the proposed chart is studied using Markov chain approach. An effect of non‐normality on cumulative sum S² chart is studied. The study reveals that the proposed cumulative sum control chart is a better alternative to parametric cumulative sum S² chart, when the process distribution is non‐normal. We provide an illustration of the proposed cumulative sum control chart.     

A new adaptive CUSUM control chart for detecting the multivariate process mean

We propose a new multivariate CUSUM control chart, which is based on self adaption of its reference value according to the information from current process readings, to quickly detect the multivariate process mean shifts. By specifying the minimum magnitude of the process mean shift in terms of its non‐centrality parameter, our proposed control chart can achieve an overall performance for detecting a particular range of shifts. This adaptive feature of our method is based on two EWMA operators to estimate the current process mean level and make the detection at each step be approximately optimal. Moreover, we compare our chart with the conventional multivariate CUSUM chart. The advantages of our control chart detection for range shifts over the existing charts are greatly improved. The Markovian chain method, through which the average run length can be computed, is also presented. Copyright © 2010 John Wiley & Sons, Ltd.     

New memory‐type dispersion control charts

The exponentially weighted moving average (EWMA) control chart is a memory‐type process monitoring tool that is frequently used to monitor small and moderate disturbances in the process mean and/or process dispersion. In this study, we propose 2 new memory‐type control charts for monitoring changes in the process dispersion, namely, the generally weighted moving average and the hybrid EWMA charts. We use Monte Carlo simulations to compute the run length profiles of the proposed control charts. The run length comparisons of the proposed and existing charts reveal that the generally weighted moving average and hybrid EWMA charts provide better protection than the existing EWMA chart when detecting small to moderate shifts in the process dispersion. An illustrative dataset is also used to show the superiority of the proposed charts over the existing chart.     

Weighted adaptive multivariate CUSUM control charts

An adaptive multivariate cumulative sum (AMCUSUM) control chart has received considerable attention because of its ability to dynamically adjust the reference parameter whereby achieving a better performance over a range of mean shifts than the conventional multivariate cumulative sum (CUSUM) charts. In this paper, we introduce a progressive mean–based estimator of the process mean shift and then use it to devise new weighted AMCUSUM control charts for efficiently monitoring the process mean. These control charts are easy to design and implement in a computerized environment compared with their existing counterparts. Monte Carlo simulations are used to estimate the run‐length characteristics of the proposed control charts. The run‐length comparison results show that the weighted AMCUSUM charts perform substantially and uniformly better than the classical multivariate CUSUM and AMCUSUM charts in detecting a range of mean shifts. An example is used to illustrate the working of existing and proposed multivariate CUSUM control charts.     

A moving average S control chart for monitoring process variability

An efficient alternative to the S control chart for detecting shifts of small magnitude in the process variability using a moving average based on the sample standard deviation s statistic is proposed. Control limit factors are derived for the chart for different values of sample size and span w. The performance of the moving average S chart is compared to the S chart in terms of average run length. The result shows that the performance of moving average S chart for varying values of w outweigh those of the S chart for small and moderate shifts in process variability.     

A control chart for monitoring the lognormal process variation using repetitive sampling

Control charts are developed to make the specific quality measures for a successful production process and follow normal distribution behaviors. But some real-life practices do not match such practices and exhibit some positively skewed behavior like lognormal distribution. The present study has considered this situation and proposed a monitoring control chart based on lognormal process variation using a repetitive sampling scheme. This concept proved better for detecting shifts as quickly as possible, and compared with the existing concept, results are elaborated through extensive tables. The average run lengths and standard deviations of the run lengths are being used as a performance evaluation measures and computed by using Monte Carlo simulations performed in R language. A real-life situation has been discussed in the example section to strengthen the proposed control chart concept in a real-life situation.     

A modified CUSUM control chart for monitoring industrial processes

Control charts are the most popular tool of statistical process control for monitoring variety of processes. The detection ability of these control charts can be improved by introducing various transformations. In this study, we have enhanced the performance of CUSUM charts by introducing a link relative variable transformation technique. Link relative variable converts the original process variable in a form which is relative to its mean. So, the link relative represents the relative positioning of the observations. Average run length (ARL ) is used to compare our technique with the previous studies. The comparison shows the overall good detection performance of our scheme for a span of shifts in the mean. A real‐world example from the electrical engineering process is also included to demonstrate the application of proposed control chart.     

Designing a parameter-free Kullback-Leibler information control chart for monitoring process mean shift

This paper proposes a parameter-free Kullback-Leibler information control chart for monitoring sustained shifts in the process mean of a normally distributed process in phase II. Two plotted statistics are provided. One is based on our backward empirical sequential test, the other is based on the maximum log-likelihood ratio change point method. These two achieve similar performances for the control chart. The performance of the proposed chart is compared with those of the cumulative sum chart, the exponentially weighted moving average chart, and the generalized likelihood ratio (GLR) chart. The results show that our proposed chart and the GLR chart have similar performances. Both can detect a wide range of shifts in the process mean, and neither requires design parameters other than the control limits. The proposed chart outperforms GLR when the size of the shift is below 1.24 standard deviations, while GLR outperforms the proposed chart when the size of the shift is above 1.24 standard deviations.     

An adaptive EWMA scheme‐based CUSUM accumulation error for efficient monitoring of process location

The examination of product characteristics using a statistical tool is an important step in a manufacturing environment to ensure product quality. Several methods are employed for maintaining product quality assurance. Quality control charts, which utilize statistical methods, are normally used to detect special causes. Shewhart control charts are popular; their only limitation is that they are effective in handling only large shifts. For handling small shifts, the cumulative sum (CUSUM) and the exponential weighted moving average (EWMA) are more practical. For handling both small and large shifts, adaptive control charts are used. In this study, we proposed a new adaptive EWMA scheme. This scheme is based on CUSUM accumulation error for detection of wide range of shifts in the process location. The CUSUM features in the proposed scheme help with identification of prior shifts. The proposed scheme uses Huber and Tukey bisquare functions for an efficient shift detection. We have used average run length (ARL) as performance indicator for comparison, and our proposed scheme outperformed some of the existing schemes. An example that uses real‐life data is also provided to demonstrate the implementation of the proposed scheme.     

An EWMA mean chart with auxiliary information

In this paper, we show that a recently proposed auxiliary information-based (AIB) adaptive EWMA (AE) chart is sensitive (not robust) to the changes in the mean of an auxiliary variable when monitoring the changes in the mean of a quality variable, called the AIB-AE chart. To circumvent the weakness of the AIB-AE chart, we develop a new AIB estimator for the mean of a quality variable that is slightly robust to the changes in the mean of an auxiliary variable. Based on this newly developed estimator, a new AIB EWMA (AIB-E) chart is proposed for monitoring the mean of a quality variable. The zero-state and steady-state average run-length profiles of the AIB-AE and AIB-E charts are estimated with Monte Carlo simulations. It is found that the AIB-E chart is not only slightly robust to the changes in the mean of an auxiliary variable, but it also outperforms the AIB-AE chart when detecting small shifts in the mean of a quality variable. Illustrative examples are also included in this study to demonstrate the implementation of the existing and proposed AIB charts.