Exact Run Length Evaluation on Extended EWMA Control Chart for Autoregressive Process

Karoon, Kotchaporn; Areepong, Yupaporn; Sukparungsee, Saowanit

doi:10.32604/iasc.2022.023322

Cited by 9 publications

(10 citation statements)

References 17 publications

(21 reference statements)

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“…The NIE method is one of the techniques that is used to approximate the ARL on a two-sided Extended EWMA chart for the trend AR(p) model. Let L N (u) be the estimated value of the ARL with the m linear equation systems by using the composite midpoint quadrature rule [16].…”

Section: Nie Methods Of Arl On a Two-sided Extended Ewma Chart For Th...mentioning

confidence: 99%

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Trend Autoregressive Model Exact Run Length Evaluation on a Two-Sided Extended EWMA Chart

Karoon¹,

Areepong²,

Sukparungsee³

2023

Computer Systems Science and Engineering

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The Extended Exponentially Weighted Moving Average (extended EWMA) control chart is one of the control charts and can be used to quickly detect a small shift. The performance of control charts can be evaluated with the average run length (ARL). Due to the deriving explicit formulas for the ARL on a two-sided extended EWMA control chart for trend autoregressive or trend AR(p) model has not been reported previously. The aim of this study is to derive the explicit formulas for the ARL on a two-sided extended EWMA control chart for the trend AR(p) model as well as the trend AR(1) and trend AR(2) models with exponential white noise. The analytical solution accuracy was obtained with the extended EWMA control chart and was compared to the numerical integral equation (NIE) method. The results show that the ARL obtained by the explicit formula and the NIE method is hardly different, but the explicit formula can help decrease the computational (CPU) time. Furthermore, this is also expanded to comparative performance with the Exponentially Weighted Moving Average (EWMA) control chart. The performance of the extended EWMA control chart is better than the EWMA control chart for all situations, both the trend AR (1) and trend AR(2) models. Finally, the analytical solution of ARL is applied to real-world data in the health field, such as COVID-19 data in the United Kingdom and Sweden, to demonstrate the efficacy of the proposed method.

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Section: Nie Methods Of Arl On a Two-sided Extended Ewma Chart For Th...mentioning

confidence: 99%

“…Zhang et al [15] proposed the ARL of a multivariate EWMA chart with Monte Carlo simulation. Karoon et al [16] developed the numerical integral equation (NIE) method for evaluating the ARL on the extended EWMA chart for the AR(p) process.…”

Section: Introductionmentioning

confidence: 99%

Trend Autoregressive Model Exact Run Length Evaluation on a Two-Sided Extended EWMA Chart

Karoon¹,

Areepong²,

Sukparungsee³

2023

Computer Systems Science and Engineering

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“…The NIE method is a technique for accurately approximating the ARL that can be used to determine the efficacy of explicit formula derivations. In this section, NTARL(u) is defined by using the NIE method with Simpson's quadrature rule [37] to estimate the ARL on the modified EWMA control chart with the IMA model and exponential white noise. The integral equation in Equation 4is solved by using a 2m +1 linear equation system on interval [l, h] with length 2m.…”

Section: -2-2-the Nie Methods For the Arl On The Modified Ewma Contro...mentioning

confidence: 99%

Detection Sensitivity of a Modified EWMA Control Chart with a Time Series Model with Fractionality and Integration

Phanthuna

Areepong

2022

Emerg Sci J

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Among the many statistical process control charts, the modified exponentially weighted moving average (EWMA) control chart has been designed to swiftly detect a small shift in a process parameter. Herein, we propose two explicit formulas for the average run length (ARL) for integrated moving average (IMA) and fractional integrated moving average (FIMA) models combined with the modified EWMA control chart for time series prediction. The application of the suggested control chart procedures depends on the residuals of the IMA and FIMA models. The performance of the control chart with both models is evaluated by using the ARL. Explicit formulas for the ARL for the two models with the modified EWMA statistic are derived and their precision is compared with the numerical integral equation method. The explicit formulas could accurately predict the true ARL while markedly decreasing the computational processing time compared to the numerical integration method. The capabilities of the IMA and FIMA models with the modified EWMA control chart were studied by varying g times the last term and exponential smoothing parameter λ, with the relative mean index being used to evaluate these situations. The results show that the modified EWMA control chart with either model performed better than the original EWMA control chart. Furthermore, the modified EWMA control chart with either model was highly efficient when g increased and λ was small. Two applications involving energy commodity prices are used to illustrate the efficacies of the proposed approaches, the results of which were in accordance with the experimental study. Doi: 10.28991/ESJ-2022-06-05-015 Full Text: PDF

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“…It is simple to use, yet achieves a significant impact on the enhancement of overall quality [3]. The awareness and knowledge of using control charting techniques to monitor a process and deliver high-quality production has grown exponentially [4][5][6]. Hence, control charts are used extensively in the manufacturing and service sectors.…”

Section: Introductionmentioning

confidence: 99%

Memory-Type Control Charts Through the Lens of Cost Parameters

Ganasan¹,

Woon²,

Mustafa³

et al. 2023

Intelligent Automation &Amp; Soft Computing

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A memory-type control chart utilizes previous information for chart construction. An example of a memory-type chart is an exponentially-weighted moving average (EWMA) control chart. The EWMA control chart is well-known and widely employed by practitioners for monitoring small and moderate process mean shifts. Meanwhile, the EWMA median chart is robust against outliers. In light of this, the economic model of the EWMA and EWMA median control charts are commonly considered. This study aims to investigate the effect of cost parameters on the out-of-control average run length ðARL 1 Þ in implementing EWMA and EWMA median control charts. The economic model was used to compute the ARL 1 parameter. The 14 input parameters were identified and the analysis was carried out based on the one-parameter-at-a-time basis. When the input parameters change based on a predetermined percentage, the ARL 1 is affected. According to the results of the EWMA chart, nine input parameters had an effect and five input parameters had no effect on the ARL 1 parameter. Further, only seven of the 14 input parameters had an effect on the ARL 1 of the EWMA median chart. However, the effect of each input parameter on the ARL 1 was different. Moreover, the ARL 1 for the EWMA median chart was smaller than the EWMA chart. This analysis is crucial to observe and determine the input parameters that have a significant impact on the ARL 1 of the EMWA and EWMA median control charts. Hence, practitioners can obtain an overview of the influence of the input parameters on the ARL 1 when implementing the EWMA and EWMA median control charts.

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Exact Run Length Evaluation on Extended EWMA Control Chart for Autoregressive Process

Cited by 9 publications

References 17 publications

Trend Autoregressive Model Exact Run Length Evaluation on a Two-Sided Extended EWMA Chart

Trend Autoregressive Model Exact Run Length Evaluation on a Two-Sided Extended EWMA Chart

Detection Sensitivity of a Modified EWMA Control Chart with a Time Series Model with Fractionality and Integration

Memory-Type Control Charts Through the Lens of Cost Parameters

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