Existing Control Charts Research Articles

Monitoring the road traffic crashes using NEWMA chart and repetitive sampling

In this paper, a control chart for neutrosophic exponentially weighted moving average (NEWMA) is designed using repetitive sampling. The application of the proposed NEWMA chart is given to monitoring road traffic crashes (RTC). The simulation study of RTC and real example of RTC showed that the proposed NEWMA chart performs better in monitoring the RTC as compared to the existing control charts. From the comparative study, it is concluded that the proposed NEWMA chart can be applied effectively to control RTC as compared to the existing charts.

Multivariate cumulative sum control chart and measure of process capability based on bivariate ranked set schemes

In this article we have proposed multivariate cumulative sum control chart based on bivariate ranked set schemes for quick identification of small variation in the process mean vector. Also, we have offered multivariate measure of process capability based on bivariate ranked set schemes for testing the customer requirements. In the construction of control chart, we have designed plotting statistic, and derived control limit. Regarding the multivariate measure of process capability, we have defined an estimator and then computed the critical values for inference purposes. In order to compare the performance of existing and proposed control charts, we have obtained various performance measures. Results reveal that performance of proposed control chart based on bivariate ranked set schemes depends on the choice of the factors such as sampling scheme, sample size, magnitude of association between concomitant variable and study variables, and size of the shift. Furthermore, comparative analysis shows that the performance of the proposed control chart based on bivariate ranked set schemes outperforms the existing methods. Finally, real life example is included in which we have applied proposed and existing control charts for monitoring calcium–magnesium and residual sodium contents in irrigation water. In addition, the implementation of the proposed multivariate measure of process capability ensures the level of calcium–magnesium and residual sodium contents in irrigation water to satisfy the requirements of customers or engineering tolerance.

A mixed HWMA‐CUSUM mean chart with an application to manufacturing process

AbstractMemory‐type control charts play a significant role to identify slight changes in the parameters of the production process. In this article, we have proposed a new cumulative sum chart that utilizes the statistic of the homogeneously weighted moving average chart. The performance of the proposed chart is studied using Monte Carlo simulations. The proposed chart is compared with some existing charts under different run length profiles. The run length profile comparisons reveal that the proposed chart performs superior as compared to the existing control charts. A real‐life application using a manufacturing process dataset is also part of this study.

Pattern Recognition of Different Window Size Control Charts Based on Convolutional Neural Network and Information Fusion

Control charts are an important tool for statistical process control (SPC). SPC has the characteristics of fluctuation and asymmetry in the symmetrical coordinate system. It is a graph with control limits used to analyze and judge whether the process is in a stable state. Its fast and accurate identification is of great significance to the actual production. The existing control chart pattern recognition (CCPR) method can only recognize a control chart with fixed window size, but cannot adjust with different window sizes according to the actual production needs. In order to solve these problems and improve the quality management effect in the manufacturing process, a new CCPR method is proposed based on convolutional neural network (CNN) and information fusion. After undergoing feature learning, CNN is used to extract the best feature set from the control chart, while at the same time, expert features (including one shape features and four statistical features) are fused to complete the CCPR. In this paper, the control charts of 10 different window sizes are generated by the Monte Carlo simulation method, and various data patterns are drawn into images, then the CCPR model is set up. Finally, simulation experiments and a real example are addressed to validate its feasibility and effectiveness. The results of simulation experiments demonstrate that the recognition method based on CNN can be used for pattern recognition for different window size control charts, and its recognition accuracy is higher than the traditional ones. In addition, the recognition method based on information fusion performs much better. The result of a real example shows that the method has potential application in solving the pattern recognition problem of control charts with different window sizes.

Monitoring the temperature through moving average control under uncertainty environment

The existing moving average control charts can be only applied when all observations in the data are determined, precise, and certain. But, in practice, the data from the weather monitoring is not exact and express in the interval. In this situation, the available monitoring plans cannot be applied for the monitoring of weather data. A new moving average control chart for the normal distribution is offered under the neutrosophic statistics. The parameters of the offered chart are determined through simulation under neutrosophic statistics. The comparison study shows the superiority of the proposed chart over the moving average control chart under classical statistics. A real example from the weather is chosen to present the implementation of the chart. From the simulation study and real data, the proposed chart is found to be effective to be applied for temperature monitoring than the existing control chart.

A Kullback‐Leibler information control chart for linear profiles monitoring

AbstractProfile monitoring is referred to as monitoring the functional relationship between the response and explanatory variables. Traditionally, process control charts monitor the mean and/or the variance of a univariate quality characteristic. For several correlated quality characteristics, multivariate process control charts monitor the mean vector and/or the covariance matrix. However, monitoring the functional relationship between variables is sometimes more beneficial. One example is the power output of a Diesel engine and the amount of fuel injected should be related. In this paper, we propose a Kullback‐Leibler information (KLI) control chart for linear profiles monitoring in Phase II. The plotted statistics of the KLI chart are calculated based on a backward procedure. The functional relationship is described by linear regression. The performance of the proposed KLI control chart is compared with those of other existing control charts, especially the Generalized Likelihood Ratio (GLR) chart for both KLI and GLR charts do not require design parameters. The results show that (1) the KLI control chart is better than the GLR control chart in detecting the shift of variance in terms of Average Time to Signal, and (2) if the shift of the regression coefficient is small, the GLR chart outperforms the KLI chart, but if the size of shift is large, the KLI chart outperforms the GLR chart. The plotted statistics of KLI are compared to that of GLR. Their similarity is discussed.

On Designing Distribution-Free Homogeneously Weighted Moving Average Control Charts

Abstract There are many practical situations in which the underlying process distribution is either completely unknown or partially known but deviates from normality. In such cases, the performance of the traditional parametric control charts deteriorates, and nonparametric control charts are considered as a robust alternative for monitoring the process. In this article, two new nonparametric homogeneously weighted moving average (NPHWMA) control charts are proposed for monitoring the deviations in process location from the target value. The proposed charts assign a specific weight to the current sample information, and the remaining weight is equally distributed among the previous samples. The proposed NPHWMA charts are based on sign test and Wilcoxon signed-rank test for process monitoring under the skewed and symmetric distributions, respectively. The Monte Carlo simulations are used to study the run length properties and compare the performance of the proposed charts with some existing control charts. It is found that the proposed charts outperform their existing counterparts. Empirical illustrations are provided for practical implementation of the proposed charts.

A hybrid homogeneously weighted moving average control chart for process monitoring

AbstractSeveral modifications and enhancements to control charts in increasing the performance of small and moderate process shifts have been introduced in the quality control charting techniques. In this paper, a new hybrid control chart for monitoring process location is proposed by combining two homogeneously weighted moving average (HWMA) control charts. The hybrid homogeneously weighted moving average (HHWMA) statistic is derived using two smoothing constants λ1 and λ2. The average run length (ARL) and the standard deviation of the run length (SDRL) values of the HHWMA control chart are obtained and compared with some existing control charts for monitoring small and moderate shifts in the process location. The results of study show that the HHWMA control chart outperforms the existing control charts in many situations. The application of the HHWMA chart is demonstrated using a simulated data.

Monitoring mean and variability by Gini chart for skew-normal distributed data

In order to monitor mean and variability of a process, the Gini control charts based on the skew-normally distributed random samples is proposed. Through comparing the false alarm rates of current scheme with those of existing mean and dispersion control charts, it is found out that the design structure of Gini chart can improve over other classic schemes based on assumption of skew-normal distribution for the data. Moreover, the superiority of the Gini chart is studied by comparing the discriminatory power curves of the skew-normal distribution with some existing control charts. Simulated studies and a real data example illustrate the usefulness of the proposed approach.

MAD Control Chart for Autoregressive Models with Skew-Normal Distribution

AbstractThe major problem in analyzing control charts is to work with autocorrelated data. This problem can be solved by fitting a suitable model to the data and using the control chart for the residuals. The problem becomes very important, when the distribution of observation is nonnormal, in addition to being autocorrelated. Much recent research has focused on the development of appropriate statistical process control techniques for the autocorrelated data or nonnormal distribution, but few studies have considered monitoring the process mean of both nonnormal and autocorrelated data. In this paper, a simulation study is conducted to compare the performances of the control chart based on the median absolute deviation method (MAD) with those of existing control charts for the skew normal distribution. Simulation results indicate considerable improvement over existing control charts for nonnormal data can be achieved when the control charts with control limits based on the MAD method are used to monitor the process mean of nonnormal autocorrelated data.

Application of Quality Control Charts for Early Detection of Flood Hazards

Flooding is a serious and devastating hazard that many countries face regularly. Timely detection of these changes can help us manage rainwater and hence flooding. Numerous statistical tools are available for the early detection of these changes. In this regard, application of control charts is an effective choice toward monitoring natural events. In this study, we used self-proposed and existing control charts as a means of early detection of changes in the rainfall data of Pakistan as a case study. The proposed methodology covered two aspects: one to enhance the ability of Shewhart control charts toward detection of small or moderate changes in the behavior of natural events, and another to offer skewness correction based on individual control chart under runs rules for managing these natural events – especially when collected data follows unknown skewed distribution. Results elucidate that control charts structures were efficient in early detection and prediction of floods during 2010. Our results are in accordance with the theoretical results of existing studies, and we propose similar methods to be used for meteorological purposes.

Phase-I monitoring of high-dimensional covariance matrix using an adaptive thresholding LASSO rule

High-dimensional variability monitoring and diagnosing is of great prominence for the quality improvement and cost reduction. Most of the existing control charts are mainly based on the assumption that the in-control covariance matrix is known in prior. This paper proposes a new control chart for monitoring of variability of high-dimensional process under the sparsity conditions. The proposed control chart uses the adaptive thresholding LASSO rule for estimating the unknown covariance matrix. To evaluate the performance of the proposed chart, named as T-COV, the signal probability was estimated under several patterns of out-of-control conditions and compared with the conditional entropy (CE) control chart. This paper uses the process of spur gear production as a real-world example to illustrate the operating procedures of the T-COV chart. The results of the simulation and real studies have revealed the advantage of the T-COV chart over the CE in quickly capturing and precisely diagnosing the deviation in the covariance matrix of the high-dimensional processes.

A double homogeneously weighted moving average control chart for monitoring of the process mean

AbstractIn the service and manufacturing industry, memory‐type control charts are extensively applied for monitoring the production process. These types of charts have the ability to efficiently detect disturbances, especially of smaller amount, in the process mean and/or dispersion. Recently, a new homogeneously weighted moving average (HWMA) chart has been proposed for efficient monitoring of smaller shifts. In this study, we have proposed a new double HWMA (DHWMA) chart to monitor the changes in the process mean. The run length profile of the proposed DHWMA chart is evaluated and compared with some existing control charts. The outcomes reveal that the DHWMA chart shows better performance over its competitor charts. The effect of non‐normality (in terms of robustness) and the estimation of the unknown parameters on the performance of the DHWMA chart are also investigated as a part of this study. Finally, a real‐life industrial application is offered to demonstrate the proposal for practical considerations.

Moving Average control charts for Burr X and Inverse Gaussian distributions

The Burr X and Inverse Gaussian (IG) distributions are considered in this paper to design an attribute control chart for time truncated life test with Moving Average (MA) scheme w. The presentation of the MA control chart is estimated in terms of average run length (ARL) by using the Monte Carlo simulation. The ARL is decided for different values of sample sizes, MA statistics size, parameters’ values, and specified average run length. The performance of this new MA attribute control chart is compared with the usual time truncated control chart for Burr X and IG distributions. The performance of a new control chart is better than the existing control chart.

A Comparative Analysis of Robust Dispersion Control Charts with Application Related to Health Care Data

Abstract One of the most efficient tools of statistical process control is the control chart. The efficiency and effectiveness of control charts depend on its in-control robustness, i.e., how the control chart reacts against the violation of the designed model of the chart. The current study evaluates the in-control robustness properties of a chart that is based on the mixture of the statistics of cumulative sum and exponentially weighted moving averages (CS-EWMA) control charts for monitoring the process dispersion under normal, nonnormal, and contaminated normal environments. The in-control robustness performance of the CS-EWMA chart is compared with some existing control charts. Moreover, the appropriate values of the design coefficients for selected charts are also determined. In-control robustness is evaluated in terms of different properties of run length distribution, such as average run length, standard deviation of the run length, and various percentile points. In addition, a real-life application of all the selected charts based on the colonoscopy procedure is considered for practical implementation. It is found that the CS-EWMA chart has a better in-control robustness performance as compared with its counterparts.

A generally weighted moving average control chart for zero‐inflated Poisson processes

AbstractZero‐inflated Poisson (ZIP) model is very useful in high‐yield processes where an excessive number of zero observations exist. This model can be viewed as an extension of the standard Poisson distribution. In this paper, a one‐sided generally weighted moving average (GWMA) control chart is proposed for monitoring upward shifts in the two parameters of a ZIP process (regarded as ZIP‐GWMA chart). The design parameters of the proposed chart are provided, and through a simulation study, it is shown that the ZIP‐GWMA performs better than the existing control charts under shifts in both parameters. Moreover, an illustrative example is presented to display the application of the proposed chart on practitioners.

A modified-mxEWMA location chart for the improved process monitoring using auxiliary information and its application in wood industry

ABSTRACT In this paper, we have proposed a new modified Exponentially Weighted Moving Average location control chart named as a modified-mxEWMA chart. The newly proposed chart uses the information of an auxiliary variable to improve the shift detection ability. The control structure of the modified-mxEWMA chart is developed and important measures such as ARL, SDRL, EQL, PCI, and RARL are computed to assess the performance of the proposed chart. A comparative analysis is carried out among the proposed modified-mxEWMA chart and some existing competitive EWMA charts. The results obtained from this study revealed that the proposed chart performs very well for the monitoring of small to moderate shifts in the process location relative to the existing control charts. Finally, a real-life data set from the wood industry is used to show the implementation procedure of the proposed chart in real applications.

Monitoring process variation using modified EWMA

AbstractA new control chart, namely, modified exponentially weighted moving average (EWMA) control chart, for monitoring the process variance is introduced in this work by following the recommendations of Khan et al.15 The proposed control chart deduces the existing charts to be its special cases. The necessary coefficients, which are required for the construction of modified EWMA chart, are determined for various choices of sample sizes and smoothing constants. The performance of the proposed modified EWMA is evaluated in terms of its run length (RL) characteristics such as average RL and standard deviation of RL. The efficiency of the modified EWMA chart is investigated and compared with some existing control charts. The comparison reveals the superiority of proposal as compared with other control charts in terms of early detection of shift in process variation. The application of the proposal is also demonstrated using a real‐life dataset.

Mixed EWMA–CUSUM chart for COM-Poisson distribution

In this article, we develop a mixed EWMA-CUSUM control chart for monitoring moderate and/or small shift in the process following the Conway Maxwell Poisson (COM-Poisson) distribution. To determine the ability and performance of the proposed mixed EWMA-CUSUM control chart, we evaluate the average run lengths and compare with different control charts. We will compare the efficiency of the proposed control chart over the existing control charts in terms of average run length. The results show an improvement in ARL when compared with the existing charts. A real example and a simulation study is also added to use the chart in the industry.

A New X-Bar Control Chart for Using Neutrosophic Exponentially Weighted Moving Average

The existing Shewhart X-bar control charts using the exponentially weighted moving average statistic are designed under the assumption that all observations are precise, determined, and known. In practice, it may be possible that the sample or the population observations are imprecise or fuzzy. In this paper, we present the designing of the X-bar control chart under the symmetry property of normal distribution using the neutrosophic exponentially weighted moving average statistics. We will first introduce the neutrosophic exponentially weighted moving average statistic, and then use it to design the X-bar control chart for monitoring the data under an uncertainty environment. We will determine the neutrosophic average run length using the neutrosophic Monte Carlo simulation. The efficiency of the proposed plan will be compared with existing control charts.