Double Exponentially Weighted Moving Average Research Articles

Evaluation of different DEWMA schemes for monitoring the ratio of two normal random variables

In many fields such as baking industry and cosmetic factory, the ratio of two normal random variables (RZ) is one of the key quality characteristics that needs to be monitored. In this paper, we study the properties of three double exponentially weighted moving average (DEWMA) schemes for monitoring the RZ. The run length (RL) properties, average run length (ARL) and standard deviation of run length (SDRL), and charting parameters of the proposed DEWMA RZ schemes are simulated for different correlation parameter between the two normal variables. These numerous simulation results are presented in tables and figures to make comparisons with the existing exponentially weighted moving average (EWMA) RZ scheme. The comparisons show that the proposed DEWMA RZ schemes are more effective than the EWMA RZ in detecting small changes. Additionally, the proposed three one-sided DEWMA RZ schemes’ properties are compared in detail. A food industry example details the implementation of the proposed RZ schemes.

Comparisons of steady‐state optimal EWMA and DEWMA charts

AbstractThe double EWMA (DEWMA) has been proposed as a more efficient control charting procedure for monitoring the mean of a process. Comparisons of the DEWMA and the EWMA charts, which often indicate the superiority of the DEWMA, are often flawed because the same smoothing constant is used in both charts. We take the approach of first selecting a shift that we would like to detect, and then compare the optimal DEWMA chart and the optimal EWMA chart for that particular shift. We consider the DEWMA chart whose smoothing constants are restricted to be the same and the general DEWMA. We find that there are situations where the optimal DEWMA outperforms, in the sense of a shorter out‐of‐control average run length (ARL) for a fixed in‐control ARL, but the improvement is slight. The optimal EWMA chart usually performs much better than the optimal DEWMA chart when the actual shift differs from the shift used to optimize the chart. The poor performance of the DEWMA chart away from the shift for which it was optimized, the nonmonotonicity of the DEWMA weights, and the additional computations required of the DEWMA chart indicate that the EWMA is a better overall choice than the DEWMA chart.

On the performance and comparison of various memory-type control charts

Several versions of the exponentially weighted moving average (EWMA) control chart, such as the generally weighted moving average (GWMA), the double, triple, and quadruple EWMA (DEWMA, TEWMA, and QEWMA), and the homogeneously weighted moving average (HWMA) charts, have been developed to enhance its detection ability, especially for small and moderate shifts. These charts have been criticized as it is considered that an appropriately designed EWMA chart provides as good or better zero-state and steady-state average run-length (ARL) performance. In this article, we perform a careful comparison study of the above control charts under similar in-control (IC) run-length properties. We show that the “new” memory-type control charts have better out-of-control (OOC) run-length characteristics, especially for small to moderate shifts in the process mean for both the zero-state and steady-state cases, except for the HWMA chart where its steady-state OOC performance is very poor. We also present a comparison study based on the worst-case ARL measure. Finally, the extensions of the EWMA chart have better IC robustness ability than the EWMA and HWMA charts.

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).

Improving Sensitivity of the DEWMA Chart with Exact ARL Solution under the Trend AR(p) Model and Its Applications

The double exponentially weighted moving average (DEWMA) chart is a control chart that is a vital analytical tool for keeping track of the quality of a process, and the sensitivity of the control chart to the process is evaluated using the average run length (ARL). Herein, the aim of this study is to derive the explicit formula of the ARL on the DEWMA chart with the autoregressive with trend model and its residual, which is exponential white noise. This study shows that this proposed method was compared to the ARL derived using the numerical integral equation (NIE) approach, and the explicit ARL formula decreased the computing time. By changing exponential parameters that were relevant to evaluating in various circumstances, the sensitivity of AR(p) with the trend model with the DEWMA chart was investigated. These were compared with the EWMA and CUSUM charts in terms of the ARL, standard deviation run length (SDRL), and median run length (MRL). The results indicate that the DEWMA chart has the highest performance, and when it was small, the DEWMA chart had high sensitivity for detecting processes. Digital currencies are utilized to demonstrate the efficacy of the proposed method; the results are consistent with the simulated data. Doi: 10.28991/ESJ-2023-07-06-03 Full Text: PDF

ARL Evaluation of a DEWMA Control Chart for Autocorrelated Data: A Case Study on Prices of Major Industrial Commodities

The double exponentially weighted moving average (DEWMA) control chart, an extension of the EWMA control chart, is a useful statistical process control tool for detecting small shift sizes in the mean of processes with either independent or autocorrelated observations. In this study, we derived explicit formulas to compute the average run length (ARL) for a moving average of order q (MA(q)) process with exponential white noise running on a DEWMA control chart and verified their accuracy by comparison with the numerical integral equation (NIE) method. The results for both were in good agreement with the actual ARL. To investigate the efficiency of the proposed procedure on the DEWMA control chart, a performance comparison between it and the standard and modified EWMA control charts was also conducted to determine which provided the smallest out-of-control ARL value for several scenarios involving MA(q) processes. It was found that the DEWMA control chart provided the lowest out-of-control ARL for all cases of varying the exponential smoothing parameter and shift size values. To illustrate the efficacy of the proposed methodology, the presented approach was applied to datasets of the prices of several major industrial commodities in Thailand. The findings show that the DEWMA procedure performed well in almost all of the scenarios tested. Doi: 10.28991/ESJ-2023-07-05-020 Full Text: PDF

Modification of ARL for detecting changes on the double EWMA chart in time series data with the autoregressive model

This research aims to derive the average run length (ARL) evaluation of the double exponentially weighted moving average (double EWMA) control chart for observation data that follows exponential white noise in a time series model with an autoregressive model. Since most real-world data is automatically correlated, autoregressive models are available. Comparisons were made between the ARLs obtained using the explicit formula and the numerical integral equation (NIE) approach. The results showed that the explicit formula's use of the ARL outperformed the NIE approach in terms of computation time. After that, the efficacy of the exponentially weighted moving average (EWMA) and double EWMA charts is then compared using the suggested explicit ARL formula. The ARL of the double EWMA chart was found to perform better than the ARL of the EWMA chart in all situations. It also uses natural gas and diesel prices on stock exchanges around the world as cases studies. The results show that the double EWMA chart has better detection sensitivity than the EWMA chart, and the results are consistent with the experimental results. As a result, the sensitivity of the double EWMA chart in detecting changes makes it a good alternative for monitoring processes with real-world data.

Reinforcement learning for process control with application in semiconductor manufacturing

Process control is widely discussed in the manufacturing process, especially in semiconductor manufacturing. Due to unavoidable disturbances in manufacturing, different process controllers are proposed to realize variation reduction. Since Reinforcement Learning (RL) has shown great advantages in learning actions from interactions with a dynamic system, we introduce RL methods for process control and propose a new controller called RL-based controller. Considering the fact that most existing run-to-run (R2R) controllers mainly rely on a linear model assumption for the process input–output relationship, we first discuss theoretical properties of RL-based controllers based on the linear model assumption. Then the performance of RL-based controllers and traditional R2R controllers (e.g., Exponentially Weighted Moving Average (EWMA), double EWMA, adaptive EWMA, and general harmonic rule controllers) are compared for linear processes. Furthermore, we find that the RL-based controllers have potential advantages to deal with other complicated nonlinear processes. The intensive numerical studies validate the advantages of the proposed RL-based controllers.

Ensemble Learning Techniques-Based Monitoring Charts for Fault Detection in Photovoltaic Systems

Over the past few years, there has been a significant increase in the interest in and adoption of solar energy all over the world. However, despite ongoing efforts to protect photovoltaic (PV) plants, they are continuously exposed to numerous anomalies. If not detected accurately and in a timely manner, anomalies in PV plants may degrade the desired performance and result in severe consequences. Hence, developing effective and flexible methods capable of early detection of anomalies in PV plants is essential for enhancing their management. This paper proposes flexible data-driven techniques to accurately detect anomalies in the DC side of the PV plants. Essentially, this approach amalgamates the desirable characteristics of ensemble learning approaches (i.e., the boosting (BS) and bagging (BG)) and the sensitivity of the Double Exponentially Weighted Moving Average (DEWMA) chart. Here, we employ ensemble learning techniques to exploit their capability to enhance the modeling accuracy and the sensitivity of the DEWMA monitoring chart to uncover potential anomalies. In the ensemble models, the values of parameters are selected with the assistance of the Bayesian optimization algorithm. Here, BS and BG are adopted to obtain residuals, which are then monitored by the DEWMA chart. Kernel density estimation is utilized to define the decision thresholds of the proposed ensemble learning-based charts. The proposed monitoring schemes are illustrated via actual measurements from a 9.54 kW PV plant. Results showed the superior detection performance of the BS and BG-based DEWMA charts with non-parametric threshold in uncovering different types of anomalies, including circuit breaker faults, inverter disconnections, and short-circuit faults. In addition, the performance of the proposed schemes is compared to that of BG and BS-based DEWMA and EWMA charts with parametric thresholds.

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.

Non-parametric progressive signed-rank control chart for monitoring the process location

In every process of the manufacturing and service industry, there exist variations. Quality practitioners desire to avoid these variations to maintain and improve the quality level of products and services. The control charts are commonly applied under the assumption of normality, however, when the underlying assumption is not valid, nonparametric (NP) control charts become alternatives for quality engineers and practitioners. In this article, an NP progressive mean control chart based on Wilcoxon signed-rank statistic (NPPM-SR) has been proposed for prompt detection of shifts in the process target. The NPPM-SR chart proves in-control robust and much effective performance in spotting deviations in the process location for heavy-tailed and skewed distributions. The run-length distribution performance of the proposed NPPM-SR chart for some selected continuous symmetrical distributions; normal, t, Laplace, logistic and contaminated normal distributions are evaluated under zero- and steady states using average run length (ARL) and some other run-length characteristics. The proposed NPPM-SR chart is compared with existing NP counterparts such as; NP exponentially weighted moving average sign (NPEWMA-SN) chart, NP EWMA based on Wilcoxon signed-rank statistic (NPEWMA-SR) chart and NP cumulative sum based on Wilcoxon signed-rank statistic (NPCUSUM-SR) chart. For the comparative analysis, the parametric competitors such as; traditional EWMA (EWMA-) chart and Double EWMA- (DEWMA-) control charts are also included in this study. The proposed NPPM-SR charting scheme under zero-state has been found efficient as compared to steady-state and its existing counterparts. The piston rings data and simulated data have been taken for the illustration of the proposal.

A New Distribution-Free Control Chart for Monitoring Process Median Based on the Statistic of the Sign Test

Abstract Control charts are used to improve the quality of outputs in manufacturing, industrial, and service processes. The parametric control charts produce more false alarms and unacceptable out-of-control signals when the underlying distribution of the process is not normal. Nonparametric/distribution-free control charts are efficient alternatives to overcome the said situation. In this article, the performance of a distribution-free double exponentially weighted moving average (EWMA) chart has been investigated based on the sign test statistic under simple and ranked set sampling schemes. The run-length properties of the proposed charts have been evaluated and compared with nonparametric EWMA sign, parametric EWMA, and parametric double EWMA control charts, using different run-length measures. The comparison reveals the efficiency of the proposed chart over its alternatives in detecting small and medium shifts in the process location. A real-data application using the substrate manufacturing process has been provided to show the implementation of the proposed chart.

A new double exponentially weighted moving average control chart for monitoring both location and dispersion

AbstractIn this article, we extend the single exponentially weighted moving average (EWMA) semicircle (EWMA‐SC) chart to a single double EWMA semicircle chart, called the DEWMA‐SC control chart. The run length (RL) characteristics of the proposed chart are computed through Monte‐Carlo simulations. A detailed comparative study is conducted to compare the performance of the proposed chart with that of the EWMA‐SC and GWMA‐SC charts with time‐varying control limits. The comparison results reveal that the DEWMA‐SC chart outperforms the competing charts in detecting most of the considered shifts in the process mean and/or variability. Additionally, the DEWMA‐SC chart shows very satisfactory overall performance for detecting a wide range of shift combinations of the process mean and dispersion, compared with the EWMA‐SC and GWMA‐SC charts assuming various control chart parameter values. Finally, real and simulated datasets are considered to present the implementation of the new chart.

A novel EWMA mean chart with its extensions

AbstractThe EWMA chart is an advanced process monitoring tool because of its sensitive nature against small and moderate shifts that occur in the process parameter(s). In this paper, with a transformation related to the Brownian motion, we propose novel EWMA, double EWMA, triple EWMA, and quadruple EWMA charts for monitoring the mean of a process that follows a normal distribution. The Monte Carlo simulations are used to compute the run length properties of the proposed charts. Based on a comparative study, it is found that the newly proposed charts are uniformly and substantially better than their existing counterparts when detecting different kinds of shifts in the process mean. Real datasets are also considered to demonstrate the implementation of the proposed charts.

The quadruple exponentially weighted moving average control chart

ABSTRACT The exponentially weighted moving average (EWMA) control chart is a very popular memory-type chart and also effective in detecting small shifts in the process mean. Several modifications of the EWMA chart, such as the double and triple EWMA charts (regarded as DEWMA and TEWMA charts, respectively) have been developed to enhance its performance in detecting small shifts. In the present article, we propose the quadruple EWMA chart (regarded as QEWMA chart) in order to improve much more the detection ability of the EWMA chart. The run-length characteristics of the proposed chart are evaluated by performing Monte Carlo simulations. Comparing with the EWMA, DEWMA and TEWMA charts, it is found that the QEWMA chart outperforms its competitors for small shifts. Moreover, it is shown that the proposed chart is more in-control (IC) robust under several non-normal distributions than the other charts, especially for a medium value of the smoothing parameter. The effect of inertia on the performance of the QEWMA chart is also investigated as a part of this article. Finally, two examples are provided to demonstrate the application of the proposed chart.

Monitoring Coefficient of Variation Using Variable Sampling Interval Double Exponentially Weighted Moving Average Charts

As a measure of relative variability, the coefficient of variation (CV) is a valuable charting statistic in statistical process control. Great efforts have been devoted to monitoring CV efficiently. To further improve the performance of CV charts, this paper proposes three Double Exponentially Weighted Moving Average (DEWMA) charts by incorporating Variable Sampling Interval (VSI) strategies to monitor the CV squared. The run length properties of the proposed charts are evaluated via Monte Carlo simulations. Comparative studies show that the proposed VSI DEWMA CV charts detect the process shifts faster than the existing CV charts. A real data example is presented to illustrate the VSI DEWMA CV charts.

An Efficient Robust Nonparametric Triple EWMA Wilcoxon Signed-Rank Control Chart for Process Location

The nonparametric (NP) control charts are famous for detecting a shift in the process parameters (location and/or dispersion) when the underlying process characteristic does not follow the distributional assumptions. Similarly, when the cost of estimations is very high and the ranking of observational is relatively simple, the ranked set sampling (RSS) technique is preferred over the simple random sampling (SRS) technique. On the other hand, the NP triple exponentially weighted moving average (EWMA) control chart based on SRS is superior to the NP EWMA and NP double EWMA (NP DEWMA) based on the SRS technique to detect a shift in the process location. This study designed an advanced form of NP TEWMA Wilcoxon signed-rank based on RSS, denoted as TEWMA − SR RSS control chart to identify a shift in the process location parameter. The Monte Carlo simulation method is used to assess the performance of the proposed TEWMA − SR RSS control chart along with SRS-based NP TEWMA (TEWMA-SR), SRS-based NP TEWMA sign (TEWMA-SN), SRS-based TEWMA − X ¯ , and RSS-based NP DEWMA-SR DEWMA − SR RSS control charts. The study shows that the proposed TEWMA − SR RSS control chart is more efficient in identifying shifts (especially in small shifts) in the process location than the existing control charts. Finally, a real-life application is also provided for the practical implementation of the proposed TEWMA − SR RSS control chart.

A Comparative Study of the EWMA and Double EWMA Control Schemes

A control scheme is the most excellent and irreplaceable tool in Statistical Process Control because of its effectiveness in controlling and monitoring the process, which indirectly helps ensure that the quality of a product is controlled. The EWMA scheme is one of the popular memory-type schemes used to control a normally distributed process. Therefore, various studies and improvements are performed on this scheme and are available in the literature. One of the significant improvements of the EWMA scheme is its extension to the double EWMA scheme, which has a better performance in detecting a small to moderate shift in the process than the traditional EWMA scheme. In order to study and compare the performance of the EWMA and double EWMA schemes in a comprehensive way, other run-length properties, such as the standard deviation and percentiles of the run-length, are also evaluated, rather than solely evaluating the average run-length results. Furthermore, the exact shift size in the process is usually not known in real life. Thus, the expected average run-length and expected median run-length metrics are used to evaluate the overall performances of these two schemes in a range of shift sizes. Then, the implementation of these two schemes is illustrated with a dataset. Last, some concluding remarks are made.

A novel cumulative EWMA‐sum mean chart

AbstractMemory‐type charts are well‐recognized as an advanced process monitoring tool because of their sensitive nature against small‐to‐moderate shifts that occur in the process parameters. One of those memory‐type charts is a CUmulative SUM (CUSUM) chart. In order to increase the sensitivity of the CUSUM mean chart, the CUSUM statistic is updated with the CUmulative EWMA‐SUM (CUESUM), which results into the CUESUM chart. The CUESUM chart encompasses the Crosier CUSUM (CCUSUM) chart. Using the Monte Carlo simulations, the run‐length properties of the CUESUM chart are computed. Based on detailed run‐length comparisons, it turns out that the CUESUM chart is more sensitive than the CCUSUM, EWMA, and double EWMA charts when detecting small shifts in the process mean. In addition, the CUESUM chart is uniformly more sensitive than the EWMA‐CUSUM chart. Real and simulated datasets are considered to demonstrate the implementation of the proposed chart.

Nonparametric Double EWMA Control Charts based on Mood Statistic for Process Variability

This research aims to propose a nonparametric double exponentially weighted moving average (NDEWMA) control chart for detecting shifts in a process using the Mood statistic. A Monte Carlo simulation study was used. The data had a normal distribution and a non-normal distribution where the magnitude of shift size (δ) was δ = 1, 1.05, 1.10 - 2.00 and 3.00, respectively. A performance comparison of the control charts was evaluated by using the Average Run Length (ARL). In the case of an in-control process, a large ARL value is desired, while a small ARL value is desired when the process is out-of-control. From the results of the simulation study, it was observed that the proposed NDEWMA control chart is effective in detecting small shifts in the process and gives better performance compared to the nonparametric exponentially weighted moving average control (NEWMA) control chart based on Mood statistics.