Mean Control Chart Research Articles

Progressive Mean as a Special Case of Exponentially Weighted Moving Average

In the category of memory‐type control charts, progressive mean control chart was proposed recently, for monitoring the process location. Here we show, through the derivation, that the plotting statistic for the progressive mean control chart becomes a special case of exponentially weighted moving average when the sensitivity parameter becomes reciprocal of the sample number. Copyright © 2014 John Wiley & Sons, Ltd.

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.

A Hybrid Learning-Based Model for Simultaneous Monitoring of Process Mean and Variance

Unnatural patterns exhibited on process mean and variance control charts can be associated separately with different assignable causes. Quick and accurate knowledge of the type of control chart patterns (CCPs), either because of process mean or variance, can greatly facilitate identification of assignable causes. Over the past few decades, however, process mean and variance CCPs are seldom studied simultaneously in the statistical process control literature. This study proposes a hybrid learning-based model for simultaneous monitoring of process mean and variance CCPs. In this model, a self-organization map neural network-based quantization error control chart is responsible for detecting the out-of-control signals, a discrete particle swarm optimization-based selective ensemble of back-propagation networks is responsible for classifying the detected out-of-control signals into categories of mean and/or variance abnormality, and two discrete particle swarm optimization-based selective ensembles of learning vector quantization networks are responsible for further identifying the detected mean and variance out-of-control signals as one of the specific CCP types, respectively. Extensive simulations indicate that the proposed hybrid learning-based model outperforms other existing approaches in detecting mean and variance changes, while also capable of CCP recognition. In addition, a case study is conducted to demonstrate how the proposed hybrid learning-based model can function as an effective tool for monitoring mean and variance simultaneously. Copyright © 2013 John Wiley & Sons, Ltd.

Improved Exponentially Weighted Moving Average Control Charts for Monitoring Process Mean and Dispersion

Exponentially weighted moving average (EWMA) control charts are mostly used to monitor the manufacturing processes. In this paper, we propose some improved EWMA control charts for detecting the random shifts in the process mean and process dispersion. These EWMA control charts are based on the best linear unbiased estimators obtained under ordered ranked set sampling (ORSS) and ordered imperfect ranked set sampling (OIRSS), named EWMA‐ORSS and EWMA‐OIRSS charts, respectively. Monte Carlo simulations are used to estimate the average run length, median run length and standard deviation of run length of the proposed EWMA control charts. It is observed that the EWMA‐ORSS mean control chart is able to detect the random shifts in the process mean substantially quicker than the Shewhart‐cumulative sum and the Shewhart‐EWMA control charts based on the RSS scheme. Both EWMA‐ORSS and EWMA‐OIRSS location charts perform better than the classical EWMA, hybrid EWMA, Shewhart‐EWMA and fast initial response‐EWMA charts. The EWMA‐ORSS dispersion control chart performs better than the simple random sampling based CS‐EWMA and other EWMA control charts in efficient detection of the random shifts that occur in the process variability. An application to real data is also given to explain the implementation of the proposed EWMA control charts. Copyright © 2013 John Wiley & Sons, Ltd.

Discrimination of Out-of-Control Condition Using AIC in (x, s) Control Chart

The x control chart for the process mean and either the R or s control chart for the process dispersion have been used together to monitor the manufacturing processes. However, it has been pointed out that this procedure is flawed by a fault that makes it difficult to capture the behavior of process condition visually by considering the relationship between the shift in the process mean and the change in the process dispersion because the respective characteristics are monitored by an individual control chart in parallel. Then, the (x, s) control chart has been proposed to enable the process managers to monitor the changes in the process mean, process dispersion, or both. On the one hand, identifying which process parameters are responsible for out-of-control condition of process is one of the important issues in the process management. It is especially important in the (x, s) control chart where some parameters are monitored at a single plane. The previous literature has proposed the multiple decision method based on the statistical hypothesis tests to identify the parameters responsible for out-of-control condition. In this paper, we propose how to identify parameters responsible for out-of-control condition using the information criterion. Then, the effectiveness of proposed method is shown through some numerical experiments.

Using Golden Ratio Search to Improve Paired Construction of Quality Control Charts

Our purpose is to indicate a new method for determining the control limits of univariate control charts to show the effectiveness of golden ratios search. We examine a solution to a problem when signals from mean and variance charts differ. Lack of concordance in the signals from mean and variance (or standard deviation) control charts bring confusion to Quality Control managers which in turn may lead to sub optimal management quality practices. To achieve better quality management practice, we provide a solution to the problem of finding different decision signals for in-control processes for quality control charts for mean and variability. We construct the control charts in experimental conditions for in-control average run length using the methods of simulation. Finally, we employ the golden ratio search method to identify the control limit parameters which differ from standard methods for constructing quality control charts. Last, we minimize the length of time in computation in the construction of these new quality control charts.

English

The information on auxiliary characteristics helps significantly in increasing the efficiency of control charts for detecting shifts in process parameters. In this study we proposed Shewhart type control charts, namely the chart, the chart and the chart, which utilizes information on two auxiliary characteristics (X and Z) for improved monitoring of process location parameter with respect to a single quality characteristic of interest (Y). Assuming trivariate normality of (Y, X, Z), a general control chart structure is developed in the form of the three sigma and the probability limits. The performance of the proposed charts is compared with the usual Shewhart chart, the chart of Riaz (2008a), the control limits of Zhang (1984) and Wade and Woodall (1993). It has been observed that the proposed charts perform superior, in terms of discriminatory power, as compared to the above mentioned counterparts, depending upon the correlation structure among the auxiliary characteristics and the quality characteristic of interest. The said superiority zone of the correlation structures, favoring the proposed charts, needs to be identified very carefully to apply it in a given situation. Key words: Auxiliary characteristics mean control charts, location parameter, normality, power curves, quality characteristics.

On efficient median control charting

In most manufacturing processes, we face sudden outliers, and in such situations, median control charts are more outliers-resistant than mean control charts. In ideal circumstances, a median chart presents less efficiency than a mean chart. In order to overcome the efficiency loss in uncontaminated environments by maintaining its resistance ability in contaminated environments, we have suggested an auxiliary information–based set of median type control charts using the coefficient of variation and coefficient of kurtosis of auxiliary characteristics for efficient process monitoring. The performances of these control charts are evaluated in terms of average run length (ARL) and extra quadratic loss (EQL) under the univariate, bivariate, and trivariate normally distributed process environments. The effects of contaminated environments are also examined on the ARL performance of different median-based charting structures. The illustrative examples concerning median type control structures are also provided for procedural details.

O efeito da autocorrelação no planejamento das cartas de controle de x̄ e EWMA

No planejamento dos gráficos de controle destinados ao monitoramento da média do processo, assume-se que esta permanece fixa em seu valor-alvo até a ocorrência de uma causa especial, que a desloca. Em muitos processos, contudo, é mais razoável supor que a média oscila mesmo na ausência de causas especiais. Para descrever este comportamento oscilatório, tem-se utilizado o modelo AR (1). Quando esta oscilação é grande, o melhor desempenho do gráfico de x̄ é obtido com amostras unitárias. O mesmo não se observa com a carta de EWMA (exceto quando o parâmetro de ponderação λ é próximo de um); os melhores desempenhos são obtidos com a adoção de amostras de tamanho n > 1 e λ pequeno, mesmo quando o objetivo é a detecção rápida de grandes deslocamentos da média. Neste estudo, tem-se utilizado como medida de desempenho o TES - tempo médio entre a ocorrência de uma mudança na posição em torno da qual a média oscila e sua sinalização pelo gráfico de controle. Quando a média do processo oscila, o TES passa a ser uma função do número esperado de visitas aos estados transientes de uma cadeia de Markov.

MONITORING THE PROCESS MEAN BASED ON QUALITY CONTROL CHARTS USING ON FOLDED RANKED SET SAMPLING

In this paper, we propose a new quality control chart for the sample mean based on the folded ranked set sampling (FRSS) method. The new charts are compared with the classical control charts using simple random sampling (SRS) and ranked set sampling (RSS). A simulation study shows that the FRSS control charts have smaller average run length (ARL) compared with their counterpart charts using SRS and RSS.

The application of mean control chart in managing industrial processes

Along with the advent of mass production comes the problem of monitoring and maintaining the quality of the product, which stressed the need for the application of selected statistical and mathematical methods in the control process. The main objective of applying the methods of statistical control is continuous quality improvement through permanent monitoring of the process in order to discover the causes of errors. Shewart charts are the most popular method of statistical process control, which performs separation of controlled and uncontrolled variations along with detection of increased variations. This paper presents the example of Shewart mean control chart with application in managing industrial process.

Nonparametric Progressive Mean Control Chart for Monitoring Process Target

Nonparametric control charts are widely used when the parametric distribution of the quality characteristic of interest is questionable. In this study, we proposed a nonparametric progressive mean control chart, namely the nonparametric progressive mean chart, for efficient detection of disturbances in process location or target. The proposed chart is compared with the recently proposed nonparametric exponentially weighted moving average and nonparametric cumulative sum charts using different run length characteristics such as the average run length, standard deviation of the run length, and the percentile points of the run length distribution. The comparisons revealed that the proposed chart outperformed recent nonparametric exponentially weighted moving average and nonparametric cumulative sum charts, in terms of detecting the shifts in process target. A real life example concerning the fill heights of soft drink beverage bottles is also provided to illustrate the application of the proposed nonparametric control chart. Copyright © 2012 John Wiley & Sons, Ltd.

Improved quality control charts for monitoring the process mean, using double-ranked set sampling methods

Statistical control charts are widely used in the manufacturing industry. The Shewhart-type control charts are developed to improve the monitoring process mean by using the double quartile-ranked set sampling, quartile double-ranked set sampling, and double extreme-ranked set sampling methods. In terms of the average run length, the performance of the proposed control charts are compared with the existing control charts based on simple random sampling, ranked set sampling and extreme-ranked set sampling methods. An application of real data is also considered to investigate the performance of the suggested process mean control charts. The findings of the study revealed that the newly suggested control charts are superior to the existing counterparts.

Progressive Mean Control Chart for Monitoring Process Location Parameter

Control charts are widely used for process monitoring. They show whether the variation is due to common causes or whether some of the variation is due to special causes. To detect large shifts in the process, Shewhart‐type control charts are preferred. Cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are generally used to detect small and moderate shifts. Shewhart‐type control charts (without additional tests) use only current information to detect special causes, whereas CUSUM and EWMA control charts also use past information. In this article, we proposed a control chart called progressive mean (PM) control chart, in which a PM is used as a plotting statistic. The proposed chart is designed such that it uses not only the current information but also the past information. Therefore, the proposed chart is a natural competitor for the classical CUSUM, the classical EWMA and some recent modifications of these two charts. The conclusion of this article is that the performance of the proposed PM chart is superior to the compared ones for small and moderate shifts, and its performance for large shifts is better (in terms of the average run length). Copyright © 2012 John Wiley & Sons, Ltd.

Statistical and economic analyses of an EWMA-based synthesised control scheme for monitoring processes with outliers

This work presents an exponentially weighted moving average (EWMA)-based synthesised control scheme for a process with outliers. Based on experience, some processes occasionally have outliers. The use of traditional mean ( X ) and range (R) control charts (denoted as X /R) for monitoring process mean and variance leads to high-level false alarms. In this study, the fast-detection technique (EWMA control chart) and robust control chart (median () control chart) are adopted. Via simulations, with various shifts in process sample mean and variance, the average time to work stoppage (ATWS) and average quality cost (AQC) for the synthesised control schemes are evaluated under some contaminated normal distributions and cost parameter settings. We conclude that, from a statistical perspective, the EWMA-based synthesised control scheme detects process shifts faster than the Shewhart-based (SB) synthesised control scheme with or without contaminated data. From an economic perspective, when the percentage of contaminated data is small or none, the EWMA-based synthesised control scheme again outperforms the SB synthesised control scheme. When the percentage of contaminated data is large, the SB synthesised control scheme performs better than the EWMA-based synthesised control scheme. This analytical result is a valuable reference for practitioners facing a process with outliers.

A new adaptive control chart for monitoring process mean and variability

Traditionally, an \(\bar{X}\) chart is used to control the process mean, and an R chart is used to control the variance. However, these charts are not sensitive to the small shifts in the processes. The adaptive charts might be considered if the aim is to detect process changes quickly. In this paper, we propose a new adaptive single control chart which integrates the exponentially weighted moving average procedure with the generalized likelihood ratio test statistics for jointly monitoring both the process mean and variability. This new chart is effective in detecting the disturbances that shift the process mean, increase or decrease the process variance, or lead to a combination of both effects.

Identifying the mean step change of UBM chart

The traditional control charts are developed based on the assumption that the successive observations are independent and identically distributed. In some processes, the independence assumption is violated when there is autocorrelation between observations. To solve this problem, two methods, classified as model-based and model-free, could be applied. When a control chart alarms an assignable cause, it is essential to detect the process change point in order to remove the root cause. In the presence of autocorrelated data, different methods for change-point identification have been applied only for model-based methods. Hence, this is considered as the research gap and an attempt is made to fill this gap by applying maximum likelihood function in unweighted batch mean control chart, one of the most applied model-free methods. In this article, an estimator is presented to determine the change point for the first-order autoregressive process, AR(1). When a real change occurs, the performance of proposed estimator is evaluated through simulation.

Effects of the two-component measurement error model on X control charts

The statistical properties of Shewhart control charts are known to be highly sensitive to measurement errors. The statistical model relating the measured value to the true, albeit not observable, value of a product characteristic, is usually Gaussian and additive. In this paper we propose to extend the said model to a more general formulation by introducing the two-component error model structure. We study the effects of the proposed error-model on the performance of the mean control charts, since gauge imprecision may seriously alter the statistical properties of the control charts. In order to take measurement errors into account in the design of the control charts we explore the use of different methods based on a weighted variance concept, a skewness correction method and an empirical reference distribution approach respectively. The different approaches are discussed and compared by Monte Carlo simulation. Results indicate that the last two methods produce the best results.

Extended maximum generally weighted moving average control chart for monitoring process mean and variability

In this paper, we propose an extended control chart, called the maximum generally weighted moving average (MaxGWMA) control chart, to simultaneously detect both increases and decreases in the mean and/or variability of a process. Simulations are performed to evaluate the average run length, standard deviation of the run length, and diagnostic abilities of the MaxGWMA and maximum exponentially weighted moving average (MaxEWMA) charts. An extensive comparison reveals that the MaxGWMA control chart is more sensitive than the MaxEWMA control chart.

A comparison study of effectiveness and robustness of control charts for monitoring process mean

This article compares the effectiveness and robustness of nine typical control charts for monitoring the mean of a variable, including the most effective optimal and adaptive Sequential Probability Ratio Test (SPRT) charts. The nine charts are categorized into three types (the X¯ type, CUSUM type and SPRT type) and three versions (the basic version, optimal version and fully adaptive (FA) version). While the charting parameters of the basic charts are determined by common wisdoms, the parameters of the optimal and fully adaptive charts are designed optimally in order to minimize an index, Average Extra Quadratic Loss ( AEQL ), for the best overall performance. A Performance Comparison Index, PCI , is also proposed as the measure of the relative overall performance of the charts. This comparison study does not only compare the detection effectiveness of the charts, but also investigate their robustness in performance. Moreover, the probability distribution of the mean shift δ is studied explicitly as an influential factor in a factorial experiment. Apart from many other findings, the results of this study reveal that the SPRT chart is more effective than the CUSUM chart and X ¯ chart by 58% and 126%, respectively, from an overall viewpoint. Moreover, it is found that the optimization design of charting parameters can increase the detection effectiveness by 29% on average, and the adaptive features can further enhance the detection power by 35%. Finally, a set of design tables are provided to facilitate the users to select a chart for their applications. ► Compare 9 control charts including X-bar, CUSUM and SPRT types and basic, optimal and adaptive versions. ► Optimization design minimizes Average Extra Quadratic Loss for the best overall performance. ► Compare not only the detection effectiveness, but also the robustness in performance. ► We found that SPRT chart is more effective than CUSUM and X-bar charts by 58% and 126%, respectively. ► Optimization design and adaptive feature increase detection effectiveness by 29% and 35%, respectively.