Modified EWMA Control Chart Research Articles

Application of Poisson state-space models and shared frailty models for multistage processes surveillance

ABSTRACT There are many applications in actual multistage processes with Poisson data. Control charts are an essential tool for monitoring quality variables in multistage processes. On the other hand, it is not straightforward to adjust a quality variable for the effect of all influential covariates, and ignoring latent variables introduces unobserved heterogeneity which diminishes the detection power of a monitoring scheme. Hence, the present paper proposes two monitoring schemes namely, the GEWMA control chart based on a Poisson state-space model and the modified EWMA control chart based on a shared frailty model in which latent variables are considered in Phase II. In this regard, expectation – maximization and Bayesian algorithms are used to estimate the parameters of the proposed models. A comparison between the two proposed control charts demonstrates that the GEWMA control chart based on a Poisson state-space model performs better than the modified EWMA control chart using the frailty model. Then, comprehensive simulation experiments are conducted to evaluate the performance of the proposed GEWMA. The results show that it performs satisfactorily under different shifts in single and multiple stages. Also, this control chart helps well to identify the out-of-control stage. Finally, a real case in health-care related processes is used to appraise the performance of the proposed monitoring scheme in practice.

Alternative to Detecting Changes in the Mean of an Autoregressive Fractionally Integrated Process with Exponential White Noise Running on the Modified EWMA Control Chart

The modified exponentially weighted moving-average (modified EWMA) control chart is an improvement on the traditional EWMA control chart. Herein, we provide more details about the modified EWMA control chart using various values of an additional design parameter for detecting small-to-moderate shifts in the process mean of an autoregressive fractionally integrated (ARFI(p, d)) process with exponential white noise running thereon. The statistical performances of the two charts were evaluated in terms of the average run length (ARL) obtained by solving integral equations (IEs). This provides an exact formula with proven existence and uniqueness verified by applying Banach’s fixed-point theorem. The accuracy of the proposed formula for the ARL was compared with the ARL derived by using the numerical IE technique for the out-of-control state. Although their accuracies were identical for various out-of-control situations and long-term memory processes, the exact formula method required less than 0.01 s to compute the ARL whereas the numerical IE method took 3–4 s. The strengths of using the exact formula are that it is simple to calculate and the computational time is significantly reduced. Comparing their standard deviations of the run length and median run lengths yielded the same results. Finally, practical examples with real-life data corresponding to ARFI(p, d) processes with exponential white noise are provided to demonstrate the applicability of the proposed exact formula.

A New Modified EWMA Control Chart for Monitoring Processes Involving Autocorrelated Data

Control charts are one of the tools in statistical process control widely used for monitoring, measuring, controlling, improving the quality, and detecting problems in processes in various fields. The average run length (ARL) can be used to determine the efficacy of a control chart. In this study, we develop a new modified exponentially weighted moving average (EWMA) control chart and derive explicit formulas for both one and the two-sided ARLs for a p-order autoregressive (AR(p)) process with exponential white noise on the new modified EWMA control chart. The accuracy of the explicit formulas was compared to that of the well-known numerical integral equation (NIE) method. Although both methods were highly consistent with an absolute percentage difference of less than 0.00001%, the ARL using the explicit formulas method could be computed much more quickly. Moreover, the performance of the explicit formulas for the ARL on the new modified EWMA control chart was better than on the modified and standard EWMA control charts based on the relative mean index (RMI). In addition, to illustrate the applicability of using the proposed explicit formulas for the ARL on the new modified EWMA control chart in practice, the explicit formulas for the ARL were also applied to a process with real data from the energy and agricultural fields.

Explicit analytical solutions for the average run length of modified EWMA control chart for ARX(p,r) processes

Explicit analytical solutions for the average run length of modified EWMA control chart for ARX(p,r) processes

Design and Application of a Modified EWMA Control Chart for Monitoring Process Mean

The modified exponentially weighted moving average (modified EWMA) control chart is an improvement on the performance of the standard EWMA control chart for detecting small and abrupt shifts in the process mean. In this study, the effect of varying the constant and exponential smoothing parameters for detecting shifts in the mean of an autoregressive process with exogenous variables (ARX(p,r)) with a trend and exponentially distributed white noise on the standard and modified EWMA control chart was investigated. The performances of the two control charts were compared via their average run lengths (ARLs) computed by using explicit formulas and the numerical integrated equation (NIE) technique. A comparative study of the two ARL methods on the modified and traditional EWMA control charts shows that the modified schemes had better detection ability at all levels of shift size. Finally, two examples using real datasets on gold and silver prices are given to illustrate the applicability of the proposed procedure. Our findings advocate that the modified EWMA chart is excellent for monitoring ARX(p,r) processes with exponentially distributed white noise

Simulation approach for assessing the performance of the γEWMA control chart

PurposeThe purpose of this paper is to evaluate the performance of a modified EWMA control chart (γEWMA control chart), which considers data distribution and incorporate its correlation structure, simulating in-control and out-of-control processes and to select an adequate value for smoothing parameter with these conditions.Design/methodology/approachThis paper is based on a simulation approach using the methodology for evaluating statistical methods proposed by Morris et al. (2019). Data were generated from a simulation considering two factors that associated with data: (1) quality variable distribution skewness as an indicator of quality variable distribution; (2) the autocorrelation structure for type of relationship between the observations and modeled by AR(1). In addition, one factor associated with the process was considered, (1) the shift in the process mean. In the following step, when the chart control is modeled, the fourth factor intervenes. This factor is a smoothing parameter. Finally, three indicators defined from the Run Length are used to evaluate γEWMA control chart performance this factors and their interactions.FindingsInteraction analysis for four factor evidence that the modeling and selection of parameters is different for out-of-control and in-control processes therefore the considerations and parameters selected for each case must be carefully analyzed. For out-of-control processes, it is better to preserve the original features of the distribution (mean and variance) for the calculation of the control limits. It makes sense that highly autocorrelated observations require smaller smoothing parameter since the correlation structure enables the preservation of relevant information in past data.Originality/valueThe γEWMA control chart there has advantages because it gathers, in single chart control: the process and modelling characteristics, and data structure process. Although there are other proposals for modified EWMA, none of them simultaneously analyze the four factors nor their interactions. The proposed γEWMA allows setting the appropriate smoothing parameter when these three factors are considered.

The performance of a modified EWMA control chart for monitoring autocorrelated PM2.5 and carbon monoxide air pollution data.

PM2.5 (particulate matter less than or equal to 2.5 micron) is found in the air and comprises dust, dirt, soot, smoke, and liquid droplets. PM2.5 and carbon monoxide emissions can have a negative impact on humans and animals throughout the world. In this paper, we present the performance of a modified exponentially weighted moving average (modified EWMA) control chart to detect small changes when the observations are autocorrelated with exponential white noise through the average run length evaluated (ARLs) by explicit formulas. The accuracy of the solution was verified with a numerical integral equation method. The efficacy of the modified EWMA control chart to monitor PM2.5 and carbon monoxide air pollution data and compare its performance with the standard EWMA control chart. The results suggest that the modified EWMA control chart is far superior to the standard one.

Identification and forewarning of GNSS deformation information based on a modified EWMA control chart

Abstract Safety of people's lives and property is an unquestionably priority of any plan for disaster mitigation and its societal impact. This study reports on a new mathematical method to process and analysis the global navigation satellite system (GNSS) data to effectively monitoring deformation of buildings. A new method combining the ensemble-integrated empirical mode decomposition (EEMD) algorithm and the EWMA control chart is proposed to identify and alert GNSS deformation information. This new approach tries to overcome the limitations affecting some classical methods like cumulative sum (CUSUM) control chart, which has a poor detection effect on continuous small offset deformation data in GNSS time series, and considering that the noise will be a certain degree inhibit the deformation information, thus affect its recognition results. The experimental results show that the recognition accuracy of the EWMA control chart method and the modified EWMA method is higher than that of the CUSUM control chart method. The modified EWMA method has the best inspection capability. The use of a modified EWMA control chart improves the accuracy of deformation information identification and early warning, which reduces the false alarm rate and missing alarm rate of disaster early warning.

The exact solution of the average run length on a modified EWMA control chart for the first-order moving-average process

The exact solution of the average run length on a modified EWMA control chart for the first-order moving-average process

A data-driven algorithm for online detection of component and system faults in modern wind turbines at different operating zones

Advanced Fault Detection (FD) and isolation schemes are necessary to realize the required levels of reliability and availability and to minimize financial losses against failures. In particular, FD is essential in modern Wind Turbine Systems (WTSs) which are designed to generate electrical energy as efficiently and reliably as possible. This paper presents a practical FD framework using data-driven methods. The main objective is the early detection of involuntary abnormalities of various types and locations. Conventional methods are based on the exact model and/or signal patterns or hardware redundancy and they generally fail to address this issue. Alternatively, the presented algorithm is motivated by the availability of fast sensors and powerful computers yielding big data which can be explored to extract and exploit useful information. In a typical WTS, FD procedures face particular challenges attributed to high levels of measurement noise and sparse changes due to the fast dynamics as well as switching control and transients. In this scope, a minimum informative set of measured variables is proposed to describe accurately and completely the system behaviour under all operating conditions. Among data-based strategies, univariate and multivariate statistical analysis tools are recommended for this approach. Principal Component Analysis (PCA) is used in this paper for its distinguished capabilities of dimensionality reduction, features de-correlation, and noise rejection. Multi PCA models are trained as a statistical reference reflecting the data variability in local zones and used in parallel for online FD. An adaptive threshold scheme, based on a modified EWMA control chart, is also used to efficiently evaluate the resulting residuals, so the overall algorithm is robust to outliers and sensitive to small and sudden abnormalities. Static and dynamic applications are investigated for FD in modern WTSs under different operation zones. The considered abnormalities span faults having different levels of severity and range from sensors and actuators to system faults. Compared to existing methods in the literature, the proposed framework demonstrates potential applications with a broader utilization scope and promising performance.

An EWMA chart for monitoring the process standard deviation when parameters are estimated

The EWMA chart for the standard deviation is a useful tool for monitoring the variability of a process quality characteristic. The performance of this chart is usually evaluated under the assumption of known parameters. However, in practice, process parameters are estimated from an in-control Phase I data set. A modified EWMA control chart is proposed for monitoring the standard deviation when the parameters are estimated. The Run Length properties of this chart are studied and its performance is evaluated by comparing it with the same chart but with process parameters assumed known.

Design and optimization of EWMA control charts for in-control, indifference, and out-of-control regions

The design of quality control charts is normally carried out considering a process shift size that is considered important to be detected. The EWMA control chart is one of the best available options to use when good performance is needed to detect small process shifts. This paper presents a method for design of EWMA charts for control processes, in which the detection of small shifts is not necessary, and at the same time is effective in detecting important shifts. In such cases the EWMA control chart can also be designed successfully to deal with these requirements. A Markov chain approach is also applied to determine the ARL of the modified EWMA control chart. The implementation and interpretations are provided and numerical examples are used to illustrate the application procedure. We also investigate some basic properties of the proposed scheme. Genetic algorithms have been used to carry out this design.