Accurate Average Run Length Analysis for Detecting Changes in a Long-Memory Fractionally Integrated MAX Process Running on EWMA Control Chart

Peerajit, Wilasinee

doi:10.37394/23206.2023.22.58

Cited by 4 publications

(1 citation statement)

References 23 publications

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“…The model assumes that there is an underlying exponential white noise. Using an analytical formula based on an integral equation, Peerajit [25] gave a precise estimation of the ARL for long-memory models in the same year. Examples of these models include fractionally integrated MAX processes (FIMAX) with exponential white noise operating on an EWMA control chart.…”

Section: Introductionmentioning

confidence: 99%

The Development and Evaluation of Homogenously Weighted Moving Average Control Chart based on an Autoregressive Process

Sunthornwat,

Sukparungsee,

Areepong

2024

HighTech. Innov. J.

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This research aims to investigate a Homogenously Weighted Moving Average (HWMA) control chart for detecting minor and moderate shifts in the process mean. A mathematical model for the explicit formulae of the average run length (ARL) of the HWMA control chart based on the autoregressive (AR) process is presented. The efficacy of the HWMA control chart is evaluated based on the average run length, the standard deviation of run length (SDRL), and the median run length (MRL). As illustrations of the design and implementation of the HWMA control chart, numerical examples are provided. In numerous instances, a comparative analysis of the HWMA control chart relative to the Extended Exponentially Weighted Moving Average (Extended EWMA) and cumulative sum (CUSUM) control charts with mean process shifts is performed in detail. Additionally, the relative mean index (RMI), the average extra quadratic loss (AEQL), and the performance comparison index (PCI) are utilized to evaluate the performance of control charts. For various shift sizes, the HWMA control chart is superior to the Extended EWMA and CUSUM control charts. This study applies empirical data from the area of economics to validate the explicit formula of ARL values for the HWMA control chart. Doi: 10.28991/HIJ-2024-05-01-02 Full Text: PDF

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Section: Introductionmentioning

confidence: 99%

The Development and Evaluation of Homogenously Weighted Moving Average Control Chart based on an Autoregressive Process

Sunthornwat,

Sukparungsee,

Areepong

2024

HighTech. Innov. J.

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Efficient Monitoring of Autoregressive and Moving Average Process using HWMA Control Chart

Areepong,

Sukparungsee,

Anusas-Amornkul

2024

Wseas Transactions on Systems

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Quality control is an essential process for manufacturing and industry because it enhances product quality, consumer satisfaction, and overall profitability. Among many other statistical process control tools, quality practitioners typically employ control charts to monitor the industrial process and detect production changes. Control charts are widely used to detect flaws in many applications, such as distributed circuits and systems, electronic devices, and systems and signals. In this study, we derived an explicit formula for Average Run Length (ARL) of the Homogenously Weighted Moving Average control chart (HWMA) under the ARMA (p,q) process. The accuracy was checked using the numerical integral equation (NIE) technique. The finding showed that the explicit formulas and numerical solutions presented an outstanding level of agreement. However, the computational time for the explicit formulas was approximately one second, which was less than that required for the NIE. Moreover, the performance efficiency of the HWMA control chart is compared with the cumulative sum control chart for ARMA (p, q) processes including ARMA (2,1), ARMA (2,3), and ARMA (1,1) processes. The results found that the HWMA control chart performance is found to be preferable to the CUSUM control chart performance. Additionally, the explicit formula of the HWMA control chart was implemented in a practical application of the count of nonconformities in printed circuit boards (PCBs).

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Approximating the ARL to Monitor Small Shifts in the Mean of an AR Fractionally Integrated with an exogenous variable Process Running on an EWMAControl Chart

Peerajit

2024

Wseas Transactions on Systems

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Control charts are used to monitor processes and detect changes in a given control scheme. The Exponential Weighted Moving Average (EWMA) control chart is a well-recognized control chart used to detect small changes in parameters. The efficiency of the chart studied is usually achieved using ARL. Approximating ARL using the Gauss-Legendre quadrature method, also known as NIE,. This approach is used to evaluate the ARL of developments, such as explicit formulas because it provides a robust way to validate their validity and accuracy. Moreover, it evaluates the performance of control charts for time series under exponential white noise. Exponential white noise is obtained from a long-memory fractionally integrated AR with exogenous variables or the long-memory ARFIX process. Under the long-memory ARFIX model, the proposed technique compares the control chart's performance to an explicit formula using the criterion of percentage accuracy. The results of the comprehensive numerical study include investigations into a wide range of out-of-control processes and situations. Specifically, the results from the accuracy percentage in all cases are more than 95%, which means that the proposed technique is accurate and completely consistent with the well-defined explicit formula. Therefore, it is recommended that it be used in this situation. There are examples from real data that were found to be consistent with the research results.

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Accurate Average Run Length Analysis for Detecting Changes in a Long-Memory Fractionally Integrated MAX Process Running on EWMA Control Chart

Cited by 4 publications

References 23 publications

The Development and Evaluation of Homogenously Weighted Moving Average Control Chart based on an Autoregressive Process

The Development and Evaluation of Homogenously Weighted Moving Average Control Chart based on an Autoregressive Process

Efficient Monitoring of Autoregressive and Moving Average Process using HWMA Control Chart

Approximating the ARL to Monitor Small Shifts in the Mean of an AR Fractionally Integrated with an exogenous variable Process Running on an EWMAControl Chart

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