Hybrid Exponentially Weighted Moving Average Research Articles

The modified control charts for monitoring the error detection of process control under different estimators 

The reflected power function distribution (RPFD) has increasing importance in practical life due to its application in diversified fields of life. Organisations often face difficulty monitoring operations to identify and remove errors during production. That is why there is a need to introduce control charts that effectively monitor the processes, mainly when the number of errors follows RPFD and the manufacturing process is in control. The current study suggested memory-based control charts as a solution to the problem. The control charts are based on the estimation methods and play a remarkable role in enhancing the machine process reliability. The parameters of RPFD are evaluated through the percentile estimator (PE) and modified maximum likelihood estimator methods (MMLM). Further, we create memory-based control charts, i.e., hybrid exponentially weighted moving average (HEWMA) and extended exponentially weighted moving average (EEWMA), using the PE and MMLM. The findings reflect that HEWMA control charts based on PE provide a better result in estimating the defects. The implications of the study will be helpful for practitioners and policy makers from reliability engineering, management sciences, and statisticians.

Control theory for skewed distribution under operation side of the telecommunication industry and hard-bake process in the semiconductor manufacturing process

Statistical process control basically involves inspecting a random sample of the output from a process and deciding whether the process is producing products with characteristics that fall within a predetermined range. It is used extensively in the field of reliability engineering. The reliability of the production process is thoroughly monitored for any internal variation using the SPC. The aim is always to settle such variations through a proper control monitoring. If the underlying distribution of the process is known to the researcher than the use of parametric control charts are useful but in many cases when there is doubt about the distribution of the process then it is preferred to use non parametric control charts. In this paper we propose the modified Exponentially weighted moving average (EWMA), Double Exponentially weighted moving average (DEWMA), Hybrid Exponentially weighted moving average (HEWMA), Extended Exponentially weighted moving average (EEWMA), Modified Exponentially weighted moving average (MEWMA) and mix- type control charts by mixing these control charts with Tukey control chart EWMA-TCC, DEWMA-TCC, HEWMA-TCC, EEWMA-TCC, MEWMA-TCC for the shape parameter of the Kumaraswamy Lehmann-2 Power function distribution (KL2PFD).

Error detection through modified phase II process monitoring under different classical estimators

In real life, the distribution of the errors during any life testing of products or process does not meet the assumption of normality. Statistical process control (SPC) is defined as the use of statistical techniques to control a process or production method. SPC tools and procedures can help to monitor process behavior, discover problems in internal systems, and find solutions for production issues. To identify and remove the variation in different reliability processes and to monitor the reliability of machines where the number of errors follows skewed distributions, we develop control charts to keep the process in control. For such situations, we have modified the existing control charts such as Shewhart control chart, exponentially weighted moving average (EWMA), hybrid exponentially weighted moving average (HEWMA) and extended exponentially weighted moving average (EEWMA) control charts. The current study introduced classical estimator based modified control charts for phase-II monitoring by assuming that the errors occur during the process follow skewed distribution called Beta Lehmann 2 Power function distribution (BL2PFD). The proposal for these control charts is based on the percentile estimator. We have compared all these control charts using Monte Carlo simulation studies and real-life applications to compare the proposed control charts. This study shows that an EEWMA control chart based on PE performs better than Shewhart, EWMA and HEWMA control charts, when the underlying distribution of the errors in process monitoring follows BL2PFD. These findings can be useful for researchers and practitioners in dealing with production errors and optimizing the output.

Hybrid EWMA Control Chart under Bayesian Approach Using Ranked Set Sampling Schemes with Applications to Hard-Bake Process

A memory-type control chart is an important tool of statistical process control for monitoring small to moderate shifts in the manufacturing process. Using the prior information by the Bayesian approach is helpful in control charts. In this paper, a new hybrid exponentially weighted moving average (HEWMA) control chart is suggested under the Bayesian theory using ranked set sampling (RSS) schemes for posterior and posterior predictive distribution with informative prior and different loss functions (LFs). The extensive Monto Carlo simulation is conducted to evaluate the overall performance of the proposed Bayesian HEWMA control chart through average-run-length (ARL) and standard-deviation of the run-length (SDRL). Finally, a numerical example of the hard-bake process in semiconductor manufacturing is used to check the working and execution of the proposed Bayesian HEWMA control-chart under different RSS schemes. The results reveal that the suggested Bayesian HEWMA control-chart under RSS schemes is more sensitive in detecting out-of-control signals than the Bayesian HEWMA and Bayesian AEWMA control-charts under simple random sampling.

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.

Comparisons of some memory‐type control chart for monitoring Weibull‐distributed time between events and some new results

AbstractMonitoring Weibull time between event (TBE) processes is essential to avoid deterioration of quality characteristics in various reliability analysis problems. Statistical process monitoring (SPM) charts are widely used to monitor the possible decreasing mean shift. For monitoring such data, many control charts have been proposed in the literature, such as the Weibull exponentially weighted moving average (EWMA) chart, the Weibull cumulative sum (CUSUM) chart, and Mixed EWMA–CUSUM (MEC) chart and Mixed Hybrid EWMA–CUSUM (MHEC) chart. The current investigation revisits their efficacy and compares them with a CUSUM chart based on the generally weighted moving average (GWMA) statistic, labelled as the Mixed GWMA–CUSUM (MGC) chart, to monitor the decreasing mean shift in Weibull TBEs processes. We offer some numerical results based on the Monte‐Carlo simulation, such as average run length (ARL), the standard deviation of the run length (SDRL) and the relative mean index (RMI). Our findings show that the MGC chart often outperforms the existing control charts in detecting small downward shifts. Finally, an illustrative example is given to display the application of the MGC chart for Weibulll data.

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 New Hybrid Exponentially Weighted Moving Average control chart using Mixture Ratio Estimator of Mean

In this paper, we propose a Hybrid Exponentially Weighted Moving Average (HEWMA) control chart based on a mixture ratio estimator of mean using a single auxiliary variable and a single auxiliary attribute (Moeen et al., [1]). We call it as Z- HEWMA control chart. The proposed control chart performance is evaluated using outof- control-Average Run Length (ARL1). The control limits of the proposed chart is based on estimator, its mean square errors. A simulated example is used to compare the proposed Z-HEWMA, traditional/simple EWMA chart and CUSUM control chart. From this study the fact is revealed that Z-HEWMA control chart shows more efficient results as compared to traditional/simple EWMA and CUSUM control charts. The Z-HEWMA chart can be used for efficient monitoring of the production process in manufacturing industries where auxiliary information about a numerical variable and an attribute is available.

A robust hybrid exponentially weighted moving average chart for monitoring time between events

AbstractMonitoring time between events () is an essential aspect of the high‐yield processes where the events of interest rarely occur. This study proposes a one‐sided scheme of a hybrid exponentially weighted moving average (HEWMA) chart for monitoring , where it is assumed that the observations follow a gamma distribution. This chart is symbolized as the chart. The chart detects the downward shift, that is, a decrease in the interarrival times that can lead to a deterioration of the process. A simulation study is carried out for the numerical results, and one‐sided chart is evaluated along with one‐sided triple (, double , , double , and charts. The results show that the one‐sided chart outperforms its rivals, particularly in the case of small‐to‐moderate downward shifts. Moreover, this study also investigated the robustness of the chart, where the true distribution of the observations is assumed to be Weibull or lognormal, and it is found that the chart is reasonably robust. Finally, two examples are given to demonstrate how to use the chart in real‐world situations.

Robust Distribution-Free Hybrid Exponentially Weighted Moving Average Schemes Based on Simple Random Sampling and Ranked Set Sampling Techniques

This paper proposes new nonparametric hybrid exponentially weighted moving average (HEWMA) control charts based on simple random sampling (SRS) and ranked set sampling (RSS) techniques using the Wilcoxon rank-sum W statistic. The in-control robustness and out-of-control (OOC) performances are thoroughly investigated using extensive simulations. The HEWMA W chart is shown to be superior to the basic exponentially weighted moving average (EWMA) and double EWMA W charts in many cases under normal and nonnormal distributions. Moreover, the OOC sensitivities of the new HEWMA W -type control charts are further improved by using supplementary 2-of-2 and 2-of-3 standard and improved runs-rules approaches. It is found that the proposed HEWMA W -type charts with runs-rules perform better than the basic HEWMA W SRS and RSS charts. Real-life data based on the impurity of iron ore are used to illustrate the design and implementation of the new control charts.

The modified control charts for monitoring the shape parameter of weighted power function distribution under classical estimator

AbstractZaka et al provided a new distribution called the Weighted Power function distribution (WPFD), which has application in reliability engineering and survival analysis. They used different estimation methods to estimate the unknown parameters of WPFD and proved that modified maximum likelihood estimator (MMLE) is best to consider for the estimation of parameters. We have constructed the memoryless and memory‐based control charts based on the assumption that the distribution of the underlying process does not follow the normal distribution. In this paper, we provide modified control charts using MMLE of the shape parameter for WPFD. We develop control charts to keep the process in control when the distribution of errors of underlying process follows WPFD. We propose the modified memoryless control chart, that is, Shewhart control chart and modified memory‐based control chart, that is, Exponentially weighted moving average (EWMA) and Hybrid exponentially weighted moving average (HEWMA) control charts. We have made the comparison of the proposed control charts using Monte Carlo simulation and the real‐life application for both and the memoryless control charts and memory‐based control charts. We see that HEWMA based on MMLE performs better as compared to other proposed control charts.

Conditional covariance matrix forecast using the hybrid exponentially weighted moving average approach

AbstractThis paper extends the hybrid multivariate exponentially weighted moving average (EWMA) approach to incorporate realized variance for conditional covariance matrix forecast. The proposed estimator employs a realized variance‐based EWMA specification to estimate the conditional variance of returns and a standard return‐based EWMA specification to estimate the correlation between each pair of returns. This hybrid realized variance‐based EWMA estimator produces forecasts of the conditional covariance matrix that are statistically more accurate and informative and economically more useful than those produced by the standard EWMA and the multivariate generalized autoregressive conditional heteroscedasticity (GARCH) models using only daily returns. The evidence of incremental forecast accuracy and the economic value over the intraday range‐based hybrid EWMA estimator is, however, insignificant. Moreover, the hybrid EWMA estimators are less sensitive to the choice of decay factors than the standard EWMA model and thus provide a robust framework to accommodate intradaily information for estimates of daily return volatility while achieving a simplicity and ease of implementation.

Control charts for the shape parameter of reflected power function distribution under classical estimators

AbstractThe reflected power function distribution (RPFD) has applications in the fields of reliability engineering and survival analysis. To identify and remove the variation in different reliability processes and also to monitor the reliability of machines where the number of errors follows RPFD, we develop control charts to keep the process in control. A memory less control chart like a Shewhart control chart, and two memory‐based control charts like an exponentially weighted moving average (EWMA) control chart and a hybrid exponentially weighted moving average (HEWMA) control chart are discussed and compared with each other. Proposal of these control charts is based on two different estimators, the percentile estimator (PE) and the modified maximum likelihood estimator (MMLE). This study shows that an HEWMA control chart based on PE performs better than PE‐based Shewhart and EWMA control charts, as well as MMLE‐based Shewhart, EWMA, and HEWMA control charts.

Control Charts for the Shape Parameter of Power Function Distribution under Different Classical Estimators

In practice, the control charts for monitoring of process mean are based on the normality assumption. But the performance of the control charts is seriously affected if the process of quality characteristics departs from normality. For such situations, we have modified the already existing control charts such as Shewhart control chart, exponentially weighted moving average (EWMA) control chart and hybrid exponentially weighted moving average (HEWMA) control chart by assuming that the distribution of underlying process follows Power function distribution (PFD). By considering the situation that the parameters of PFD are unknown, we estimate them by using three classical estimation methods, i.e., percentile estimator (P.E), maximum likelihood estimator (MLE) and modified maximum likelihood estimator (MMLE). We construct Shewhart, EWMA and HEWMA control charts based on P.E, MLE and MMLE. We have compared all these control charts using Monte Carlo simulation studies and concluded that HEWMA control chart under MLE is more sensitive to detect an early shift in the shape parameter when the distribution of the underlying process follows power function distribution.

Improved Hybrid Exponentially Weighted Moving Average Control Chart using Auxiliary Information

Statistical process control is an important tool for maintaining the quality of a production process. Several control charts are available to monitor changes in process parameters. In this study, a control chart for the process mean is proposed. For this purpose, an auxiliary variable is used in the form of a regression estimator under the configuration of the hybrid exponentially weighted moving average (HEWMA) control chart. The proposed chart is evaluated by conducting a simulation study. The results showed that the proposed chart is sensitive with respect to the HEWMA chart. A real-life application is also presented to demonstrate the performance of the proposed control chart.

HYBRID EXPONENTIALLY WEIGHTED MOVING AVERAGE (HEWMA) CONTROL CHART BASED ON EXPONENTIAL TYPE ESTIMATOR OF MEAN

In this paper, we have proposed a Hybrid Exponentially Weighted Moving Average (HEWMA) control chart. The proposed control chart is based on the exponential type estimator for mean using two auxiliary variables (cf. Noor-ul-Amin and Hanif, 2012). We call it an EHEWMA control chart because it is based on the exponential estimator of the mean. From this study, the fact is revealed that E-HEWMA control chart shows more efficient results as compared to traditional/simple EWMA chart and DS.EWMA control chart (cf. Raza and Butt, 2018). The comparison of the E-HEWMA control chart is also performed with the DS-EWMA chart. The proposed chart also outperforms the other control chartsin comparison. The E-HEWMA chart can be used for efficient monitoring of the production process in manufacturing industries.A simulated example has been used to compare the proposed and traditional/simple EWMA charts and DS.EWMA control chart. The control charts' performance is measured using the average run length-out of control (ARL1). It is observed that the proposed chart performs better than existing EWMA control charts.

Design of hybrid EWMln-S2 control chart

ABSTRACTMemory type control charts have built using logarithmic transformations for the normalization of unbiased sample variance for monitoring of changes in the dispersion of process. The intention of this study is to give a new hybrid exponentially weighted moving average (HEWMA) control chart for monitoring theprocess dispersion. The logarithmic transformation is used to normalize the distribution of sample variance. The execution of the proposed HEWMA control chart is evaluated in accordance with the average run length and standard deviation run length estimated with the help of Monte Carlo method. The proposed HEWMTn control chart has been compared with the corresponding existing charts to detect increase and decrease in the process variability. It showed that the proposed HEWMTn control chart is uniformly better than its parallels for detection of shifts in the process variability. A numerical study is also given to understand the operationalization of the proposed control chart.

A robust alternate to the HEWMA control chart under non-normality

ABSTRACT In practice, a hybrid exponentially weighted moving average (HEWMA) control chart for monitoring the process mean based on the normality assumption. The performance of control chart is seriously affected if quality characteristics depart from normality or have the presence of outliers. For such situations, a new robust-HEWMA control chart is proposed for the scenario in which quality characteristics being monitored follow symmetric not necessarily normal as well as skewed phenomena. The generalized least-squares (GLS) algorithm based on order statistics is integrated to determine the control limits for non-normal process. Consequently, the process mean is unbiased and has the minimum variance in spite of non-normality. Moreover, for the long-tailed symmetric and skewed processes, the GLS estimators through their systematic coefficients structures provide robust estimates. To utilize this advantage, we have investigated the impact of data contamination and the estimators used in Phase I on the performance of proposed robust HEWMA control chart in the Phase II. Finally, we provide two real-life examples along with the simulation studies to show the implantation of our proposed chart.

Generally weighted moving average control charts using repetitive sampling

Generally weighted moving average (GWMA) control charts have been validated for effective detection of small process shifts, and perform better than exponentially weighted moving average (EWMA) control charts. These charts are available based on single sampling; however, repetitive sampling charts have received less attention. Here, a GWMA control chart based on repetitive sampling (namely an RS-GWMA chart) is proposed for enhancing detectability of small process shifts. Simulations show that the proposed RS-GWMA chart with large design and small adjustment parameters outperforms existing hybrid EWMA (HEWMA) control charts based on repetitive sampling. An in-silico example is considered for demonstrating the applicability of the proposed RS-GWMA chart.

A hybrid EWMA chart using coefficient of variation

PurposeThe purpose of this paper is to develop a new control chart using two EWMA statistics called the hybrid exponentially weighted moving average (HEWMA) chart to improve the sensitivity of EWMA chart proposed by Zhang et al. (2014). When mean and variance of process are not constants, the use of control chart using coefficient of variation (CV) is a successful approach.Design/methodology/approachThe control chart using EWMA statistics has ability to detect moderate and small shifts in the process. The authors present the designing of the proposed HEWMA statistics control chart called the HEWMACV chart based on two hybrid EWMA (HEWMA) statistics. The proposed control chart utilizes the current information and previous information to make decision about the state of control chart.FindingsIn this paper, the authors will present the designing of HEWMA statistics control chart called the HEWMACV chart. The efficiency of the proposed control chart is shown using the simulated data and real data from the industry. The application of proposed chart on the real data shows that the proposed chart has ability to detect shift in the process and it is superior than existing chart in terms of average run length (ARL).Research limitations/implicationsThe design and implementation of the proposed control chart on a real data shows that it can be applied in several industries, such as chemical industry, biological assays, etc.Practical implicationsThe practical application of HEWMA chart using coefficient variation is gaining extensive adequacy. The design and implementation of the HEWMA chart offers a new approach in the detection of small process mean shift.Originality/valueIn practice, when mean and variance of process are not constants, the use of control chart using CV is a successful approach. In this paper, the authors designed a new control chart using two EWMA statistics called the HEWMA chart to improve the sensitivity of EWMA chart. The comparison shows that the proposed chart is superior than the existing chart in terms of ARL.