Proposed Control Chart Research Articles

An improved mixed-homogeneously weighted moving average-CUSUM control chart for efficient monitoring of a process mean

Some memory-based control charts such as cumulative sum (CUSUM) control chart, exponentially weighted moving average (EWMA) control chart, and homogeneously weighted moving average (HWMA) control chart are used to monitor small-to-moderate shift in the process mean. An HWMA control chart is a memory-based enhanced version of an EWMA control chart because it detects smaller shifts earlier than an ordinary EWMA control chart. The use of auxiliary information-based HWMA statistic enhances the efficiency of a usual CUSUM control chart. This study intends to present an efficient version of usual CUSUM control chart by utilizing an auxiliary information-based HWMA statistic as input information into usual CUSUM control chart. Supremacy of the proposed control chart is established on the basis of average run length (ARL), percent decrease in ARL (PDARL), and Friedman rank test (FRT) by conducting a Monte Carlo simulation. A real-life application shows the implementation of the proposed control chart.

MONITORING INVERSE RAYLEIGH DISTRIBUTED LIFETIMES USING DEWMA CONTROL CHART

In this paper, we proposed a Double Exponentially Weighted Moving Average DEWMA control chart. The proposed control chart is based on Inverse Rayleigh Distributed lifetimes using simple random sampling. Out-of-control-Average Run Length (ARL1) is used to evaluate the performance of the proposed control chart. The DEWMA control chart is compared with traditional/simple EWMA and CUSUM control charts. A simulated example is used to compare the proposed DEWMA, traditional/simple EWMA chart control chart. It is observed that the proposed DEWMA control chart performs simple EWMA control charts. The DEWMA control chart can be used for efficient monitoring of the production process in manufacturing industries where the data is coming from inverse Rayleigh Distribution. Keywords: EWMA, CUSUM, DEWMA, average run length (ARL).

Constructing control charts for autocorrelated data using an exhaustive systematic samples pooled variance estimator

SPC with positive autocorrelation is well known to result in frequent false alarms if the autocorrelation is ignored. The autocorrelation is a nuisance and not a feature that merits modeling and understanding. This paper proposes exhaustive systematic sampling, which is similar to Bayesian thinning except no observations are dropped, to create a pooled variance estimator that can be used in Shewhart control charts with competitive performance. The expected value and variance are derived using quadratic forms that is nonparametric in the sense no distribution or time series model is assumed. Practical guidance for choosing the systematic sampling interval is offered to choose a value large enough to be approximately unbiased and not too big to inflate variance. The proposed control charts are compared to time series residual control charts in a simulation study that validates using the empirical reference distribution control limits to preserve stated in-control false alarm probability and demonstrates similar performance.

Modified calibrated control charts for monitoring the population mean under stratified sampling

AbstractIn this research paper, we discuss the use of calibration technique to propose some new estimators under stratified sampling design and its use in reliability engineering. We first proposed the estimators using the calibration technique and then modify the already existing control charts such as Shewhart, exponentially weighted moving average and hybrid exponentially weighted moving averages using these calibration estimators. We also have studied the use of the proposed control charts in detail by showing their efficiency in terms of average run length. We find out that a hybrid control chart is more effective to detect the early shifts in the mean of the process.

Robust online detection on highly censored data using a semi-parametric EWMA chart

For time and cost considerations, high censoring rate is quite common in life tests, which is a critical issue in lifetime monitoring. Conventional control charts designed for highly censored data are commonly based on the Weibull distribution. However, the distribution assumption may not be valid in practice, which brings challenges to the monitoring procedures. Motivated by this, a semi-parametric exponential weighted moving average (EWMA) control charting procedure is developed for highly censored lifetime data of any distribution. The control scheme uses the Kaplan–Meier estimator to construct the cumulative distribution function (CDF) and generalized Pareto distribution to improve the tail estimation. Then a Kolmogorov–Smirnov statistic defined by the differences between the in-control CDF and the empirical CDF is integrated into an EWMA charting scheme to monitor the Type I right-censored sample. We use simulation studies and a real-data analysis to show the efficiency of the proposed control chart.

Control Charts for Monitoring the Mean of Skew-Normal Samples

The presence of asymmetric data in production processes or service operations has prompted the development of new monitoring schemes. In this article, an adapted version of the exponentially weighted moving averages (EWMA) control chart with dynamic limits is proposed to monitor the mean of samples from the skew-normal distribution. The detection ability of the proposed control chart in online monitoring was investigated by simulating the average run length (ARL) performance for different out-of-control scenarios. The results of the simulation study suggest that the proposed scheme overcomes the main drawback of the recently developed Shewhart-type control scheme. As shown in this article, the existing Shewhart-type procedure exhibits the undesirable property of taking longer to detect changes in the mean value of skewed normal observations due to increases in the shape parameter of the basic distribution than in stable conditions. The proposed control chart was shown to work fairly acceptably in all considered out-of-control scenarios.

Robust Point M-Scale Estimators for Monitoring the Mean of EWMA Control Chart under the Normal Process

The Exponentially Weighted Moving Average (EWMA) control chart is well known in statistical process control (SPC) for identifying small shifts in process parameters. In general, the EWMA control chart is focused on data set estimates of the process characteristics under study. In this research, for observing the process mean, we modify the control limits of the EWMA control chart by using robust point M-scale estimators under the normal process. We compare five robust point M-scale estimators proposed in SPC literature, namely Sn, Qn, MAD, Tauτ^ and FQn. The traditional control limits are evaluated and distinctions are also made based on true process control limits. The control charts performances under study are estimated via a Monte-Carlo simulation analysis by calculating the interval widths (IWs) and optimal out-of-control average run length (ARL1). From the simulation studies results, it is seen that although all proposed and traditional control limits are closely approximating the true limits of the process but the proposed control limits based on robust FQn, Tauτ^ and MAD estimators are comparatively more stringent for detecting the small shifts in process mean. Moreover the results demonstrates that at optimal size of interval L, the control charts based on MAD, Tauτ^ as well as FQn estimators demonstrate higher sensitivity in comparison to the traditional control chart based on sample standard deviation (S) and proposed control charts based on QnandSn estimators in terms of having smaller ARL1 values. The OC curves of ARL1 indicate similar findings. For the purposes of illustration, a real-life data set is analyzed that also confirms our conclusions from the simulation analysis to a certain degree.

Optimized np Attribute Control Chart Using Triple Sampling

This paper studies an attribute control chart for monitoring the number of nonconforming items using a triple sampling (TS-np) which has not yet been applied to attribute control charts. The chart design and procedure for the decision about the state of the process are given. Mathematical expressions for the average run length (ARL) for in-control and out-of-control processes and the average sample number (ASN) are given. A bi-objective genetic algorithm that seeks to minimize the ASN and the probability of type 2 error is implemented in order to optimize the design of the TS-np control chart. A comparison between TS-np, single sampling np (SS-np), double sampling np (DS-np), and multiple dependent state repetitive sampling (MDSRS) control charts is carried out in terms of the out-of-control average run length (ARL1). Tables of ARL1 values for TS-np are presented in comparison with MDSRS and DS-np for various scenarios. The operation of the proposed control chart is shown through simulated data. Finally, it is concluded that the proposed TS-np chart has a better performance in terms of ARL1 detecting small and moderate shifts in the process nonconforming rate in-control (p0) compared with MDSRS and DS-np.

Monitoring unweighted networks with communities based on latent logit model

Nowadays it is common to see information exchange among certain nodes in various network systems such as Internet of Things (IoT) and social networks. Once anomalies occur in a network system, the interaction frequency will increase or decrease abruptly. Detecting such changes has attracted much attention in the field of statistical process control (SPC). However, limited number of research incorporate the heterogeneity and community information of nodes simultaneously. The loss of information refrains the control chart from detecting network anomalies in a timely manner. In this regard, we propose a logit model with latent factors of nodes and communities to describe the variation of communications within unweighted networks, where the presence and absence of communication between each pair of nodes is regarded as a Bernoulli variable. Then the proposed model is expressed in a matrix form to enable easy parameter estimation and derivation of monitoring statistic. A new control chart is established based on generalized likelihood ratio test (GLRT). The simulation results and two real examples demonstrate the effectiveness and advantages of proposed control chart in comparison with two alternative methods.

Comparing the performance of Kernel PCA Mix Chart with PCA Mix Chart for monitoring mixed quality characteristics

Along with the development of information and technology, the quality characteristics of a product cannot be monitored separately in the different types of control charts. In the past, conventional control charts were developed to monitor only one type of quality characteristic. The variable control charts are used to observe the variable or metric quality characteristics. Meanwhile, in monitoring non-metric characteristics or categorical data, attribute control charts are employed. To accommodate these two types of data, the PCA Mix control chart is suggested to simultaneously monitor these two types of data in one chart. However, some drawbacks occur when this chart is applied to monitor non-metric data which has an imbalanced proportion. Therefore, the Kernel PCA Mix control chart is created to overcome the gaps that occurred in the PCA Mix chart. Similar to the previous chart, this chart is also constructed using Hotelling’s T2 statistics with Kernel Density Estimation control limit. Several simulations are used to evaluate the performance of the proposed control charts. The simulation results show that the proposed chart has a better result than the previous control chart, especially for a small mean shift with an imbalanced proportion of non-metric data. However, the PCA Mix chart has a similar performance to the proposed chart when it is applied to monitor the balanced proportion of categorical data with a large mean shift. The application with simulated data with various scenarios and the real-world case also shows that the Kernel PCA Mix chart performs better compared to the performance of the PCA Mix chart.

A phase II EWMA chart for the balanced one‐way random effects model

AbstractStatistical process control (SPC) techniques are used in applications where more than one sources of variation are present, for example, in a one‐way random effects (variance components) model. The Shewhart control charts for this situation have been studied by several researchers. However, exponentially weighted moving average (EWMA) charts are generally recommended in Phase II, as they are more sensitive to detecting smaller process mean shifts. We consider EWMA charts for the one‐way random effects model in the balanced case, properly accounting for the effects of parameter estimation while designing and implementing the control charts. In the sequel we derive and calculate the corrected (adjusted) control limits for Phase II applications. Following the recent literature, the limits are formulated under two perspectives, the unconditional and the conditional. Tabulations of the charting constants are provided under both perspectives along with an illustration with some actual data. A simulation study examining in‐control (IC) robustness performance is conducted under both perspectives. Finally, some conclusions are given. An R package is provided to support deployment of the proposed control chart in practice.

A Distribution-Free THWMA Control Chart under Ranked Set Sampling

The basic assumption of the parametric control charts is that the underlying process follows the specific distribution. The appropriateness of parametric control charts is questionable when different industrial applications do not support this desired assumption. Recently, nonparametric control charts have been introduced to overcome this deficiency of parametric control charts. Nonparametric control charts have the same in-control run-length characteristics for all continuous distributions and are in-control robust. On the other hand, the ranked set sampling technique is preferred over the simple random sampling technique with control charts because it reduces variability and improves the control chart’s performance. So, this study aims to propose a nonparametric triple homogenously weighted moving average control chart under Wilcoxon signed-rank test with a ranked set sampling technique (regarded as NPTHWMA RSS ) to further enhance the process location monitoring. Monte Carlo simulations are used for computational purposes. The proposed control chart’s run-length performance is compared with competing control charts, like TEWMA-SR, TEWMA- X ¯ , TEWMA-SN, TEWMA- SR RSS , and NPDHWMA RSS control charts. The comparison revealed that the proposed NPTHWMA RSS control chart outperformed the other competing control charts, particularly for small to moderate shifts in process location. Finally, a real-life application is presented for quality practitioners to illustrate the effectiveness of the proposed control chart.

Improved adaptive EWMA control chart for process location with applications in groundwater physicochemical parameters and glass manufacturing industry.

The adaptive exponentially weighted moving average (AEWMA) control charts are the advanced form of classical memory control charts used for efficiently monitoring small-to-large shifts in the process parameters (location and/or dispersion). These AEWMA control charts estimate the unknown shifts using exponentially weighted moving average (EWMA) or cumulative sum (CUSUM) control charts statistics. The hybrid EWMA (HEWMA) control chart is preferred over classical memory control charts to detect early shifts in process parameters. So, this study presents a new auxiliary information-based (AIB) AEWMA (IAEWMAAIB) control chart for process location that estimates the unknown location shift using HEWMA statistic. The objective is to develop an unbiased location shift estimator using HEWMA statistic and then adaptively update the smoothing constant. The shift estimation using HEWMA statistic instead of EWMA or CUSUM statistics boosts the performance of the proposed IAEWMAAIB control chart. The Monte Carlo simulation technique is used to get the numerical results. Famous performance evaluation measures like average run length, extra quadratic loss, relative average run length, and performance comparison index are used to evaluate the performance of the proposed chart with existing counterparts. The comparison reveals the superiority of the proposed control chart. Finally, two real-life applications from the glass manufacturing industry and physicochemical parameters of groundwater are considered to show the proposed control chart’s implementation procedure and dominance.

Control charts for profile monitoring of within-profile correlations using the Tweedie exponential dispersion process model

In some manufacturing processes, the quality of a product can be characterized by the functional relationship between the response variable and the explanatory variables. Profile monitoring is a tool used to examine the stability of the functional relationship over time. Many studies have pointed out that the measurements within a profile are uncorrelated. In this research, to take advantage of the ability to provide a comprehensive description of a wide variety of data, the Tweedie exponential dispersion process model is used to account for the within-profile correlation. Then, two exponentially weighted moving average control charts are developed to detect process changes during a Phase II application. In the simulation studies, we showed that our proposed control charts outperform the existing methods for monitoring linear and nonlinear profiles. Finally, two numerical examples are given to demonstrate the usefulness of our proposed control charts.

Simultaneous monitoring of mean vector and covariance matrix of auto‐correlated multivariate multiple linear profiles

AbstractThe aim of this paper is to develop control charts for a simultaneous monitoring of the mean vector and covariance matrix of multivariate multiple linear regression profiles in phase II, when the independence assumption of the observations within each profile is violated, and there is multivariate autoregressive moving average (MARMA)(1,1) autocorrelation structure within each profile. A transformation method is applied to eliminate the autocorrelation, and six control charts for a simultaneous monitoring of the mean vector and covariance matrix of auto‐correlated multivariate multiple linear regression profiles are proposed. Then, through simulation runs, in terms of the average run length (ARL) criterion, it is shown that the proposed methods have better performance in comparison with the competing methods in detecting shifts in the parameters of regression profiles. Finally, the application of the proposed control charts is shown using real data in a machining process.

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.

A resubmission-based variable control chart

In this paper, an attempt is made to develop a new variable control chart under the resubmitted sampling scheme. The resubmission of a sample allows retaking a sample to pass through inspection/analyzing if there is a question on the inspection of the sample at any stage. The proposed control chart includes the X-bar chart as a special case. The performance of the proposed control chart is assessed by determining the in-control and out-of-control average run lengths for the various parametric settings. For illustrative purposes, a real-life example is presented to explain a detailed implementation of the proposed control chart.

Attribute Control Chart for Rayleigh Distribution Using Repetitive Sampling under Truncated Life Test

A control chart is an important tool in statistical process monitoring that is useful to monitor and improve production process quality. In this article, an attribute control chart using repetitive sampling under a truncated life test is proposed for monitoring the mean life of the product where the lifetime follows the Rayleigh distribution. The repetitive sampling parameters and the control limit coefficients of the chart are determined so that the in-control average run length (ARL) is very close to the target ARL. Tables of ARL values for various shift sizes in the scale parameter were presented, and the performance of the proposed chart is compared with the existing attribute control charts using the out-of-control ARL. The proposed control chart is shown to outperform the existing control charts in terms of ARL. An illustrative example is given to demonstrate the application of the proposed chart.

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.