Explicit analytical solutions for <i>ARL</i> of CUSUM chart for a long-memory SARFIMA model

Peerajit, Wilasinee; Areepong, Yupaporn; Sukparungsee, Saowanit

doi:10.1080/03610918.2017.1408821

Cited by 8 publications

(5 citation statements)

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“…An approximate ARL using the numerical IE method via Fredholm's integral equation of the second kind was previously formulated for a CUSUM control chart by Peerajit et al [22]. For this method, an approximate ARL was developed by using the Gauss-Legendre quadrature rules technique.…”

Section: The Numerical Arl For a Sarfimax(p D Q R) S Process With Und...mentioning

confidence: 99%

“…To evaluate the ARL for a SARMA(1, 1) s process with exponential white noise on a CUSUM control chart, Phanyaem [21] developed explicit formulas for IEs initially based on the SARMA model. In addition, analytical IEs for the solution for the ARL for a long-memory SARFIMA model on CUSUM control chart were presented by Peerajit et al [22]. Recently, complex data from seasonal and non-seasonal MA processes with exogenous variables were used to evaluate the ARL on a CUSUM control chart by Sunthornwat and Areepong [23].…”

Section: Introductionmentioning

confidence: 99%

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Integral equation solutions for the average run length for monitoring shifts in the mean of a generalized seasonal ARFIMAX(P, D, Q, r)s process running on a CUSUM control chart

Areepong

Peerajit

2022

PLoS ONE

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The CUSUM control chart is suitable for detecting small to moderate parameter shifts for processes involving autocorrelated data. The average run length (ARL) can be used to assess the ability of a CUSUM control chart to detect changes in a long-memory seasonal autoregressive fractionally integrated moving average with exogenous variable (SARFIMAX) process with underlying exponential white noise. Herein, new ARLs via an analytical integral equation (IE) solution as an analytical IE and a numerical IE method to test a CUSUM control chart’s ability to detect a wide range of shifts in the mean of a SARFIMAX(P, D, Q, r)s process with underlying exponential white noise are presented. The analytical IE formulas were derived by using the Fredholm integral equation of the second type while the numerical IE method for the approximate ARL is based on quadrature rules. After applying Banach’s fixed-point theorem to guarantee its existence and uniqueness, the precision of the proposed analytical IE ARL was the same as the numerical IE method. The sensitivity and accuracy of the ARLs based on both methods were assessed on a CUSUM control chart running a SARFIMAX(P, D, Q, r)s process with underlying exponential white noise. The results of an extensive numerical study comprising the examination of a wide variety of out-of-control situations and computational schemes reveal that none of the methods outperformed the IE. Specifically, the computational scheme is easier and can be completed in one step. Hence, it is recommended for use in this situation. An illustrative example based on real data is also provided, the results of which were found to be in accordance with the research results.

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Section: The Numerical Arl For a Sarfimax(p D Q R) S Process With Und...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Integral equation solutions for the average run length for monitoring shifts in the mean of a generalized seasonal ARFIMAX(P, D, Q, r)s process running on a CUSUM control chart

Areepong

Peerajit

2022

PLoS ONE

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“…Sunthornwat et al [12] estimate the fractional differencing parameter and the optimal smoothing value for the EWMA control chart to assess the Average Run Length (ARL) and compare the analytical EWMA and CUSUM control charts. Peerajit et al [13] recently proposed explicit formulas for the average run length (ARL) of the CUSUM chart for non-seasonal and seasonal ARFIMA models. The accuracy of explicit ARL was compared with the numerical integral equation (NIE) method based on the Gauss-Legendre quadrature rule.…”

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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“…A process should be monitored using statistical means to determine whether a shift occurs, and action should be taken once the process is considered out-of-control (OC) [15][16][17][18]. Many researchers have discussed and proposed many useful charts, such as Shewhart charts [19,20], cumulative sum (CUSUM) charts [21][22][23][24][25][26][27][28][29][30], and exponentially weighted moving average (EWMA) charts [31][32][33][34][35][36][37][38], to detect whether there is a change in quality characteristics in a process. These proposed control schemes can be used for data analysis, including control and forecasting, which are useful for fault diagnosis in practice.…”

Section: Introductionmentioning

confidence: 99%

A New Nonparametric Multivariate Control Scheme for Simultaneous Monitoring Changes in Location and Scale

Jin

Liu

2022

Computational and Mathematical Methods in Medicine

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Real-time monitoring of the breast cancer index is becoming increasingly important. It can help create advances in the diagnosis and treatment of breast cancer. In today’s modern medical processes, simultaneously monitoring changes in observations in terms of location and scale are convenient for the implementation of control schemes but can be challenging. In this paper, we consider a new nonparametric control scheme for monitoring location and scale parameters in multivariate processes. The proposed method is easy to implement, and the performance of the proposed control procedure is discussed. Then, we compare the proposed scheme with some competing methods. Simulation results show that the proposed scheme can efficiently detect a range of shifts. The proposed chart can trigger an alert and timely discover the change of the breast cancer index.

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Explicit analytical solutions for ARL of CUSUM chart for a long-memory SARFIMA model

Cited by 8 publications

References 0 publications

Integral equation solutions for the average run length for monitoring shifts in the mean of a generalized seasonal ARFIMAX(P, D, Q, r)s process running on a CUSUM control chart

Integral equation solutions for the average run length for monitoring shifts in the mean of a generalized seasonal ARFIMAX(P, D, Q, r)s process running on a CUSUM control chart

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

A New Nonparametric Multivariate Control Scheme for Simultaneous Monitoring Changes in Location and Scale

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