Average Control Chart Research Articles

New modified exponentially weighted moving average-moving average control chart for process monitoring

The mixed control chart is proposed to improve detection performance with fewer process shifts. In this study, we proposed the modified exponentially weighted moving average - moving average control chart (MMEM), a new mixed control chart for observing the changes in the process mean. Average run length, standard deviation of run length, and median run length can be used to examine the effectiveness of detecting changes in the proposed chart with Shewhart, Moving Average (MA), Modified Exponentially Weighted Moving Average (MEWMA), and Mixed Moving Average - Modified Exponentially Weighted Moving Average (MMME) control charts in parametric and nonparametric distributions that use Monte Carlo simulation. The results demonstrate that the proposed chart outperforms other control charts mostly in the detection of small-to-moderate shifts. To illustrate the application of the proposed chart, chemical process temperature data and dataset on survival times of a group of patients suffering from head and neck cancer disease and treated with radiotherapy were provided, and it was discovered that the proposed chart performs better than other control charts.

Monitoring the Ratio of Two Normal Variables Based on Triple Exponentially Weighted Moving Average Control Charts with Fixed and Variable Sampling Intervals

In statistical process control (SPC), the ratio of two normal random variables (RZ) is a valuable statistical indicator to be taken as the charting statistic. In this work, we propose a triple exponentially weighted moving average (TEWMA) chart for monitoring the RZ. Additionally, the variable sampling interval (VSI) strategy has been adopted to different control charts by researchers. With the application of this strategy, the VSI-TEWMA-RZ chart is then developed to further improve the performance of the proposed TEWMA-RZ chart. The run length (RL) properties of the proposed TEWMA-RZ and VSI-TEWMA-RZ charts are obtained by the widely used Monte-Carlo (MC) simulations. Through the comparisons with the VSI-EWMA-RZ and the VSI-DEWMA-RZ charts, the VSI-TEWMA-RZ chart is statistically more sensitive than the VSI-EWMA-RZ and the VSI-DEWMA-RZ charts in detecting small and moderate shifts. Moreover, it turned out that the VSI-TEWMA-RZ chart has better performance than the TEWMA-RZ chart on the whole. Furthermore, this paper illustrates the implementation of the proposed charts with an example from the food industry.

Application of Statistical Process Control for Structural Health Monitoring of a High-Speed Railway Track System

To make full use of the massive monitoring data accumulated in China high-speed railways, an improved statistical process control (SPC) framework was introduced to analyze the discontinuous monitoring data of the track system on a high-speed railway elevated station. Multilinear regression models and time series difference equation (TSDE) models were first developed to separate common-cause variations in the monitoring data. Then, individual control charts, moving range control charts, and exponentially weighted moving average control charts were constructed to detect special-cause variations. Results showed that the variations of girder displacement and track slab–girder relative displacements mainly resulted from temperature effects and linear trends related with material damages. Moreover, visible serial dependence was found in the regression model residuals, which could be effectively captured by the TSDE model. Numerous outliers were detected at the measuring points of rail–track slab displacement 15 and track slab–girder relative displacement 17 by more than three control charts, implying higher sensitivity to special causes. With respect to the special causes triggering the anomalous responses of local and overall track systems, sixteen and twenty-eight significant special events were detected, respectively.

Improved Nonparametric Control Chart Based on Ranked Set Sampling with Application of Chemical Data Modelling

The statistical performance of parametric control charts is questionable when the underlying process does not follow any specified probability distribution. Nonparametric control charts are the best substitute for this situation. On the other hand, the ranked set sampling technique is preferred over the simple random sampling technique because it reduces the variability of process parameters and improves the control chart’s performance. This study aims to offer a nonparametric double homogeneously weighted moving average control chart under Wilcoxon signed-rank test considering the ranked set sampling technique (regarded as NPDHWMA RSS ), to further enhance the process location monitoring. The proposed chart’s run-length performance is compared with competing control charts, such as DEWMA- X ¯ , NPDEWMA-SR, NPRDEWMA-SR, DHWMA, and NPHWMA RSS control charts. The comparison revealed that the proposed NPDHWMA RSS control chart outperformed the other competing control charts, particularly for small to moderate shifts in process location. Finally, a real-life application is also offered for quality practitioners to show the strength of the proposed control chart.

An Adaptive EWMA Control Chart Based on Principal Component Method to Monitor Process Mean Vector

The special causes of variations, which is also known as a shift, can occur in a single or more than one related process characteristics. Statistical process control tools such as control charts are useful to monitor shifts in the process parameters (location and/or dispersion). In real-life situation, the shift is emerging in different sizes, and it is hard to identify it with classical control charts. Moreover, more than one process of characteristics required special attention because they must monitor jointly due to the association among them. This study offers two adaptive control charts to monitor the different sizes of a shift in the process mean vector. The novelty behind this study is to use dimensionally reduction techniques such as principal component analysis (PCA) and an adaptive method such as Huber and Bi-square functions. In brief, the multivariate cumulative sum control chart based on PCA is designed, and its plotting statistic is utilized as an input in the classical exponentially weighted moving average (EWMA) control chart. The run length (RL) properties of the proposed and other control charts are obtained by designing algorithms in MATLAB through a Monte Carlo simulation. For a single shift, the performance of the control charts is assessed through an average of RL, standard deviation of RL, and standard error of RL. Likewise, overall performance measures such as extra quadratic loss, relative ARL, and the performance comparison index are also used. The comparison reveals the superiority over other control charts. Furthermore, to emphasize the application process and benefits of the proposed control charts, a real-life example of the wind turbine process is included.

On Reassessment of the HWMA Chart for Process Monitoring

In the recent literature of process monitoring, homogeneously weighted moving average (HWMA) type control charts have become quite popular. These charts are quite efficient for early detection of shifts, especially of smaller magnitudes, in process parameters such as location and dispersion. A recent study pointed out a few concerns related to HWMA charts that mainly relate to its steady-state performance. It needs to be highlighted that the initial studies on HWMA focused only on the zero-state performance of the chart relative to other well-known memory charts. This study reinvestigates the performance of the HWMA chart under zero and steady states at various shifts. Using the Monte Carlo simulation method, a detailed comparative analysis of the HWMA chart is carried out relative to the exponentially weighted moving average (EWMA) chart with time-varying limits. For several values of design parameters, the in-control and out-of-control performance of these charts is evaluated in terms of the average run length (ARL). It has been observed that the structure of the HWMA chart has the ability to safeguard the detection ability and the run-length properties under various delays in process shifts. More specifically, it has been found that HWMA chart is superior to the EWMA chart for several shift sizes under zero state and is capable of maintaining its dominance in case the process experiences a delay in shift. However, the steady-state performance depends on the suitable choice of design parameters. This study provides clear cut-offs where HWMA and EWMA are superior to one another in terms of efficient monitoring of the process parameters.

Double Moving Average Control Chart for Autocorrelated Data

The assumption of normality and independence is necessary for statistical inference of control charts. Misleading results are obtained if the traditional control chart technique is applied on the auto-correlated data. When data is correlated, a time series model is employed to produce an optimum output. The objective is to create a new control chart methodology that takes the autocorrelation of observations into account. Charts of Moving Average, Exponentially Weighted and Cumulative Sum better perform in the existence of autocorrelation data for small and moderate changes. The proposed methodology is highly skilled and receptive to minor, moderate and major changes in the process. Propsed DMA chart increases efficiency of average run length (ARL) chart for moving average (MA) to detect the small to medium magnitude shifts in the mean. The simulation also demonstrates that the DMA chart with spans of w=10 and 15 generally performs well in terms of average run length (ARL) as compared to clasical MA. This research may be extended to a multivariate autocorrelated statistical process control, but it can also be used to recognise and categorise seven categories of traditional control chart patterns, such as Downward, Upward Shift, Normal Trend, Cyclic, Systematic patterns, Increasing and Decresing Trend. In order to identify and categorize a set of subclasses of abnormal patterns, this model (multivariate autocorrelated statistical process control chart) should employ a multilayer feed forward Artificial Neural Network (ANN) architecture controlled by a back-propagation learning rule.

Efficient Auxiliary Information–Based Control Charting Schemes for the Process Dispersion with Application of Glass Manufacturing Industry

The hybrid exponentially weighted moving average (HEWMA) control chart is an enhanced version of the EWMA control chart that monitors the process parameters effectively. Similarly, the auxiliary information-based (AIB) EWMA control charts are very efficient for monitoring process parameters. The purpose of this paper is to propose two new control charts for the improved monitoring of process dispersion referred to as HEWMA AIB 1 and HEWMA AIB 2 control charts. A simulation study is carried out to assess the performance of the proposed HEWMA AIB 1 and HEWMA AIB 2 control charts. Average run length, extra quadratic loss, relative average run length, and performance comparison index are used to compare the performance of the proposed control charts against the existing counterparts. The comparisons reveal the superiority of the proposed control charts against other competing control charts, particularly for small to moderate shifts in the process dispersion. Finally, a real-life data set from the glass industry is used to demonstrate the practical implementation of the proposed control charts.

A bootstrap method for the measurement error estimation in Gauge R&R$R{\&}R$ Studies

AbstractA measurement system fit for use is an essential resource to perform quality control activities: its assessment must be carried out periodically to quantify its bias(location) and precision(width) error to qualify it for the purpose it is used. In particular, the measurement system capability must be determined to evaluate how much of the observed variability originates from the gauge's precision error. Gauge Repeatability and Reproducibility () studies are aimed at getting a reliable estimate of the precision error of the measurement system. The outcome of a Gauge study are point estimates and confidence intervals of the precision error components and related measurement capability metrics. Here, a general bootstrap‐based procedure is proposed to get confidence interval estimations of the measurement error and its components from a Gauge () study for continuous observations carried out with either the Average and Range (ARGG) control chart or the experimental design method. An application of the proposed bootstrap‐method is presented for a dataset of observations.

Performance of the CUSUM Control Chart Using Approximation to ARL for Long- Memory Fractionally Integrated Autoregressive Process with Exogenous Variable

The cumulative sum (CUSUM) control chart is a well-known process monitoring tool that is sensitive to small-to-moderate changes in process parameters. In this paper, we propose an approximated average run length (ARL) method based on the numerical integral equation (NIE) method for monitoring the mean of a long-memory autoregressive fractionally integrated process with an exogenous variable (ARFIX) running on a CUSUM control chart. The approximated ARL based on the NIE method is realized by solving a system of linear equations and integration based on the partitioning and summation of the area under the curve of a function derived by using the Gauss-Legendre quadrature. In a comparative study with the ARL based on analytical formulas, the proposed approximated ARL method could detect shifts of various sizes in the process mean of an ARFIX process running on a CUSUM control chart. In addition, the proposed method was compared with their analytical formulas in terms of the relative percentage change (r%) to verify the accuracy of the ARL results. The results revealed that the ARL results obtained from the NIE method are an approach to analytical formulas with r% of less than 0.25. Hence, the NIE method is very accurate and in excellent agreement with the analytical formulas approach. Apparently, the NIE method is an alternative as efficiently as the analytical method for this situation. It also performed well in comparison with the approximated ARL for the same process running on an exponentially weighted moving average control chart. In addition, real datasets are also used to demonstrate the efficacy of the proposed method.

On the Average Run Lengths of Quality Control Schemes Using a Numerical Integral Equation Approach

This research presents the approach of estimating the average run length (ARL) by using the numerical integral equation (NIE) approach, such as the Gaussian, Midpoint, Trapezoidal, and Simpson’s rules for the extended exponentially weighted moving average (EEWMA) control chart, when observations are continuous distributions namely exponential, Weibull and Gamma distributions. In addition, the performance of the extended exponentially weighted moving average (EEWMA) control chart is compared with the modified exponentially weighted moving average (modified EWMA) and exponentially weighted moving average (EWMA) control charts. The performance metric is the out-of-control average run length (ARL1). The results show that the EEWMA control chart performs the best among the modified EWMA and EWMA control charts. Furthermore, the efficacies of the control charts using the approximated ARL solutions were also applied to real-world applications.

A Study of Batting out-of-form in One-Day International Cricket

When a batter scores low in a series of innings, lack of self-confidence generated as a result coupled with poor batting strategies may lead to scoring even lower in the immediately preceding innings. In a team game like Cricket, the out-of-form status of a batter may affect the outcome of the game. This motivated us to explore a statistical method to detect batting inconsistency of a batter in Cricket. One-sided Exponentially weighted moving average (EWMA) control chart was employed due to its evident capability in rapid detection of upward or downward changes in the process mean. The analysis of this study considered ODI batters, who were engaged in the sport during the past decade belonging to seven different cricket nations. An observation of out-of-control state in a control chart was recognized as a batter experiencing an out-of-form performance phase and basic sensitizing rules were utilized to detect non-random and unnatural variation which were explained as warning signals of batting inconsistency. As a demonstration of the proposed method, EWMA control charts of a few popular batters were presented and analyzed which revealed some interesting findings related to their ODI career performance. When an occurrence of a clear downward sequence was detected in the control chart, it was decided that the batter has been out-of-form during that phase. The proposed method can be utilized to dynamically evaluate career batting performance through detection of out-of-form status of batsmen using their recent past scores and this would facilitate effective player selection for the next game.

Exact Run Length Computation on EWMA Control Chart for Stationary Moving Average Process with Exogenous Variables

The exponentially weighted moving average (EWMA) control chart is a popular tool used to monitor and identify slight unnatural variations in the manufacturing, industrial, and service processes. In general, control charts operate under the assumption of normality observation of the attention quality feature, but it is not easy to maintain this assumption in practice. In such situations, the data of random processes are correlated data, such as stock price in the economic field or air pollution data in the environment field. The characteristics and performance of the control chart are measured by the average run length (ARL). In this article, we present the new explicit formula of ARL for EWMA control chart based on MAX(q,r) process. The proposed explicit formula of ARL for the MAX(q,r) process is proved using the Fredholm integral equation technique. Moreover, ARL values are also assessed using the numerical integral equations method based on Gaussian, midpoint, and trapezoidal rules. Banach's fixed point theorem guarantees the existence and uniqueness of the solution. Furthermore, the accuracy of the proposed explicit formula is assessed in absolute percentage relative error compared with the numerical integral equations method. The results found that the explicit formula's ARL values are similar to those obtained using the numerical integral equation method; the absolute percentage relative errors are less than 0.0001 percent. As a result, the essential conclusion is that the explicit formula outperforms the numerical method in computational time. Consequently, the proposed explicit formula and the numerical integral equation have been the alternative approaches for computing ARL values of the EWMA control chart. They would be applied in various fields, including economics, environment, biology, engineering, and others.

Veterinary syndromic surveillance using swine production data for farm health management and early disease detection

The use of syndromic surveillance (SyS) has grown in animal health since the 2010s, but the use of production data has been underexplored due to methodological and practical challenges. This paper aimed to tackle some of those challenges by developing a SyS system using production data routinely collected in pig breeding farms. Health-related indicators were created from the recorded data, and two different time-series types emerged: the weekly counts of events traditionally used in SyS; and continuous time-series, where every new event is a new observation, and grouping by time-unit is not applied. Exponentially Weighted Moving Average (EWMA) and Shewhart control charts were used for temporal aberration detection, using three detection limits to create a “severity” score. The system performance was evaluated using simulated outbreaks of porcine respiratory and reproduction syndrome (PRRS) as a disease introduction scenario. The system proved capable of providing early detection of unexpected trends, serving as a useful health and management decision support tool for farmers. Further research is needed to combine results of monitoring multiple parallel time-series into an overall assessment of the risk of reproduction failure.

A double generally weighted moving average control chart for monitoring the process variability

In the present article, a double generally weighted moving average (DGWMA) control chart based on a three-parameter logarithmic transformation is proposed for monitoring the process variability, namely the -DGWMA chart. Monte-Carlo simulations are utilized in order to evaluate the run-length performance of the -DGWMA chart. In addition, a detailed comparative study is conducted to compare the performance of the -DGWMA chart with several well-known memory-type control charts in the literature. The comparisons indicate that the proposed one is more efficient in detecting small shifts, while it is more sensitive in identifying upward shifts in the process variability. A real data example is given to present the implementation of the new -DGWMA chart.

Improved control chart performance using cautious parameter learning

Parameter estimation is an important topic in Statistical Process Monitoring, as inaccurate estimates may lead to undesirable control chart performance. Updating the control chart limits during the monitoring period reduces estimation uncertainty. However, when out-of-control situations remain undetected, using the corresponding samples to update the parameter estimates can deteriorate the control chart performance in terms of in-control and out-of-control run lengths. For this reason, updating parameter estimates should only occur when there is sufficient evidence of an in-control process state. In this article, we study the performance of a cautious updating scheme for the Shewhart, Cumulative Sum, and Exponentially Weighted Moving Average control charts. We propose simple rules for updating parameters that improve the out-of-control performance of the control charts. We show the added value of using these updating rules in practice through a case study using data from a truck manufacturer.

Exponential Weight Moving Average (EWMA) Control Chart for Quality Control of Crude Palm Oil Product

In several cases of product quality control in manufactur industries, data that has a small average shift is found due to autocorrelated data, which is a state where the data currently taken is influenced by previous data. The commonly used control chart - the Shewhart control chart, does not show the real situation in the company. The Exponential Moving Weight Average (EMWA) control map is used as an alternative control map to detect small average shifts. In measurement of quality of Crude Palm Oil Product, such as Free Fatty Acid content and level of Colour, where the sampling points are the same, or the samples used are the same, but are collected at different times, this situation could happen. As a result, predictions based on control charts are sometimes not in accordance with real conditions. This study aims to compare the EMWA control chart with the Shewart control chart in analizing the quality of a product. The product used was crude palm oil (CPO) with a case study data from PT X laboratories, a palm oil processing company in Dumai, Riau. We compared the performance of EWMA Control Chart with basic Shewart Control Chart and found that EWMA Control Chart give best performance and much shorter of out of control data.

Monitoring Betaine Using Interval Time Between Events Control Chart.

A generalization of moving average (MA) control chart for the exponential distribution under classical statistics is presented in this article. The designing of the MA control chart for the exponential distribution under neutrosophic statistics is also presented. A Monte Carlo simulation under neutrosophic is introduced and applied to determine the neutrosophic control limits coefficients and neutrosophic average run length and neutrosophic standard deviation for various shifts. The application of the proposed chart is given using Betaine data. The comparison and real example studies show the efficiency of the proposed chart over the existing charts.

Evaluation of the learning curve for conformal sphincter preservation operation in the treatment of ultralow rectal cancer

BackgroundTo investigate the learning curve of conformal sphincter preservation operation (CSPO) in the treatment of ultralow rectal cancer and to further explore the influencing factors of operation time.MethodsFrom August 2011 to April 2020, 108 consecutive patients with ultralow rectal cancer underwent CSPO by the same surgeon in the Department of Colorectal Surgery of Changhai Hospital. The moving average and cumulative sum control chart (CUSUM) curve were used to analyze the learning curve. The preoperative clinical baseline data, postoperative pathological data, postoperative complications, and survival data were compared before and after the completion of learning curve. The influencing factors of CSPO operation time were analyzed by univariate and multivariate analysis.ResultsAccording to the results of moving average and CUSUM method, CSPO learning curve was divided into learning period (1–45 cases) and learning completion period (46–108 cases). There was no significant difference in preoperative clinical baseline data, postoperative pathological data, postoperative complications, and survival data between the two stages. Compared with the learning period, the operation time (P < 0.05), blood loss (P < 0.05), postoperative flatus and defecation time (P < 0.05), liquid diet time (P < 0.05), and postoperative hospital stay (P < 0.05) in the learning completion period were significantly reduced, and the difference was statistically significant. Univariate and multivariate analysis showed that distance of tumor from anal verge (≥ 4cm vs. < 4cm, P = 0.039) and T stage (T3 vs. T1-2, P = 0.022) was independent risk factors for prolonging the operation time of CSPO.ConclusionsFor surgeons with laparoscopic surgery experience, about 45 cases of CSPO are needed to cross the learning curve. At the initial stage of CSPO, beginners are recommended to select patients with ultralow rectal cancer whose distance of tumor from anal verge is less than 4 cm and tumor stage is less than T3 for practice, which can enable beginners to reduce the operation time, accumulate experience, build self-confidence, and shorten the learning curve on the premise of safety.

The performance of double exponentially weighted moving average control charts for monitoring the coefficient of variation

The coefficient of variation (CV) is one of the most important quality characteristics in industrial applications. There have been some control charts for monitoring this dimensionless and normalized characteristic. This paper presents three double exponentially weighted moving average (DEWMA) charts for monitoring the CV. Many numerical simulations are performed and the results are given in several tables to show the properties of the proposed DEWMA CV charts. Through comparisons with other existing exponentially weighted moving average (EWMA) CV charts using the average run length (ARL) metric, it is shown that the proposed DEWMA CV charts perform better than the existing EWMA CV charts for small shifts, especially when the smoothing parameter increases. In addition, a detailed comparison among the proposed three DEWMA CV charts is also presented. A real date example from industry is used to show the implementation of the proposed charts.