Average run length of the long-memory autoregressive fractionally integrated moving average process of the exponential weighted moving average control chart

Sunthornwat, Rapin; Areepong, Yupaporn; Sukparungsee, Saowanit

doi:10.1080/23311835.2017.1358536

Cited by 13 publications

(16 citation statements)

References 16 publications

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“…Petcharat et al [26] presented explicit formulas for the ARL of random observations from a MA process with exponential white noise running on a CUSUM control chart; they compared the computational times of the explicit formulas and the NIE method and found that using the former was much faster. Sunthornwat et al [27] proposed explicit formulas for the analytical ARL on an EWMA control chart with a long-memory ARFIMA model by using a solution for the integral equation and compared them with the NIE method; once again, the computational time for the former was much lower. Sunthornwat and Areepong [28] derived explicit formulas for the ARL for seasonal and non-seasonal MA processes with exogenous variables running on a CUSUM control chart and found their optimal parameters.…”

Section: -Literature Reviewmentioning

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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Section: -Literature Reviewmentioning

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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“…A SARFIMAX process involving real data was run on both CUSUM and EWMA control charts. The performances of the control charts were compared in terms of the ARL for detecting small to moderate shifts in the process mean; the ARL constructed using the analytical IE was used on the CUSUM control chart whereas the one using the numerical IE method was used on the EWMA control chart [28]. For the performance comparison, boundary values b = 17.37735, 19.2241 for the CUSUM control chart and b = 0.2507646, 0.2725181 for the EWMA control chart were used with prespecified ARL 0 = 370 or ARL 0 = 500, and smoothing parameter λ for the EWMA control chart was determined as 0.1.…”

Section: Plos Onementioning

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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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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“…For example, observations from environmental, health, manufacturing, and financial data are found to possess long memory. 21,35,36 The ARIMA models are not suitable for handling autocorrelation in long memory processes. 37 Therefore, this paper seeks to provide modified runs rules Shewhart charts that are capable of considering autocorrelation in long memory process monitoring.…”

Section: Introductionmentioning

confidence: 99%

Monitoring the mean of autocorrelated data with long memory from cable production using one‐sided runs rules schemes with ARFIMA (1,d,1) model

Babatunde,

Khoo,

Saha

et al. 2024

Quality & Reliability Eng

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Classical control charts were developed with the assumption that the quality characteristics being monitored are independent. However, observations from several time‐dependent processes, such as industrial or manufacturing, are bound to be autocorrelated such that their autocorrelations decay gradually (long memory) rather than exponentially (short memory). Runs rules monitoring schemes have been proposed in Statistical Process Control literature to monitor processes in the presence of autocorrelation by incorporating the autoregressive integrated moving average (ARIMA) class of models which can only handle autocorrelation with a short memory. This paper therefore incorporates the autoregressive fractionally integrated moving average (ARFIMA (1,d,1)) model into four one‐sided runs rules schemes to monitor the mean of an autocorrelated process with long memory. The performance of these four one‐sided schemes was assessed using average run length (ARL) and expected ARL (EARL) metrics. Based on the ARL and EARL of the improved runs rules (IRR) schemes, the IRR5‐of‐5 and IRR2‐of‐7 were found to issue an out‐of‐control signal faster than the corresponding standard runs rules (RR) schemes, RR5‐of‐5 and RR2‐of‐7, respectively. Also, the four one‐sided schemes IRR5‐of‐5, IRR2‐of‐7, RR5‐of‐5, and RR2‐of‐7 in their steady state condition perform better than their corresponding zero state condition. We further observed that as the fractional parameter d increases, the detection ability of the monitoring schemes reduces. The application of the four one‐sided schemes was demonstrated on the diameter of cable production.

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Average run length of the long-memory autoregressive fractionally integrated moving average process of the exponential weighted moving average control chart

Cited by 13 publications

References 16 publications

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

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

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

Monitoring the mean of autocorrelated data with long memory from cable production using one‐sided runs rules schemes with ARFIMA (1,d,1) model

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