Shewhart control chart for monitoring the mean of Poisson mixed integer autoregressive processes via Monte Carlo simulation

Sales, Lucas O. F.; Pinho, André Luís Santos de; Vivacqua, Carla A.; Ho, Linda Lee

doi:10.1016/j.cie.2019.106245

Cited by 13 publications

(6 citation statements)

References 37 publications

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“…Therefore, the monitoring of INAR(1) models has received much attention. The related research includes but not limited to the control charts for the generally developed Poisson INAR(1) models (Weiß [ 22 ], Weiß and Testik [ 23 ], Weiß and Testik [ 24 ], Yontay, Weiß, Testik and Bayindir [ 25 ]), for zero-inflated or zero-deflated INAR(1) models (Rakitzis, Weiß and Castagliola [ 26 ], Li, Wang and Sun [ 27 ], Fernandes, Bourguignon and Ho [ 28 ]), for the mixed INAR(1) model (Sales, Pinho, Vivacqua and Ho [ 29 ]), etc. While, to the best of our knowledge, methods for monitoring the zero-inflated INAR(1) model with random coefficient have not been studied in the literature so far, which is exactly what we are going to explore.…”

Section: Introductionmentioning

confidence: 99%

Monitoring the Zero-Inflated Time Series Model of Counts with Random Coefficient

Liu

Cui

Wang

2021

Entropy

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In this research, we consider monitoring mean and correlation changes from zero-inflated autocorrelated count data based on the integer-valued time series model with random survival rate. A cumulative sum control chart is constructed due to its efficiency, the corresponding calculation methods of average run length and the standard deviation of the run length are given. Practical guidelines concerning the chart design are investigated. Extensive computations based on designs of experiments are conducted to illustrate the validity of the proposed method. Comparisons with the conventional control charting procedure are also provided. The analysis of the monthly number of drug crimes in the city of Pittsburgh is displayed to illustrate our current method of process monitoring.

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Section: Introductionmentioning

confidence: 99%

Monitoring the Zero-Inflated Time Series Model of Counts with Random Coefficient

Liu

Cui

Wang

2021

Entropy

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“…The second method is to revise the upper and lower control limits of control charts to achieve an expected performance. [9][10][11][12][13][14][15][16][17][18] The third approach is to use residual control charts. [19][20][21][22][23][24][25][26] In this case, the residuals are obtained by subtracting predicted values from observed values.…”

Section: Introductionmentioning

confidence: 99%

“…First-order autoregressive (AR(1)) or vector autoregressive (VAR(1)) models are mostly used for modeling autocorrelated observations. 6,8,13,16,17,[21][22][23][24][25][26][27] With the rapid development of artificial intelligences, machine learning methods such as neural networks and hidden Markov models (HMMs) are also employed in SPC in the presence of observation autocorrelation. 26,[28][29][30][31][32][33] In the implementation of the control charts of residuals based on AR (1) or VAR(1) models, the observations have often been assumed to be first-order autocorrelated.…”

Section: Introductionmentioning

confidence: 99%

“…Also, because only every 10th data is used, the discovery of process shifts may be delayed. The second method is to revise the upper and lower control limits of control charts to achieve an expected performance 9–18 . The third approach is to use residual control charts 19–26 .…”

Section: Introductionmentioning

confidence: 99%

“…In order to obtain predicted values, appropriate prediction models are necessary. First‐order autoregressive ( AR (1)) or vector autoregressive ( VAR (1)) models are mostly used for modeling autocorrelated observations 6,8,13,16,17,21–27 . With the rapid development of artificial intelligences, machine learning methods such as neural networks and hidden Markov models (HMMs) are also employed in SPC in the presence of observation autocorrelation 26,28–33 …”

Section: Introductionmentioning

confidence: 99%

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On autoregressive model selection for the exponentially weighted moving average control chart of residuals in monitoring the mean of autocorrelated processes

Pan

Yan

2020

Quality & Reliability Eng

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With the development of automation technologies, data can be collected in a high frequency, easily causing autocorrelation phenomena. Control charts of residuals have been used as a good way to monitor autocorrelated processes. The residuals have been often computed based on autoregressive (AR) models whose building needs much experience. Data have been assumed to be firstorder autocorrelated, and first-order autoregressive (AR(1)) models have been employed to obtain residuals. But for a pth-order autocorrelated process, how the AR(1) model affects the performance of the control chart of residuals remains unknown. In this paper, the control chart of exponentially weighted moving average of residuals (EWMA-R) is used to monitor the pth-order autocorrelated process. Taking the mean and standard deviation of run length as performance indicators, two types of EWMA-R control charts, with their residuals obtained from the pth-order autoregressive AR(p) and AR(1) models, respectively, are compared. The results of the numerical experiment show that for detecting small mean shifts, EWMA-R control charts based on AR(1) models outperform ones based on AR(p) models, whereas for detecting large shifts, they are sometimes slightly worse. A practical application is used to give a recommendation that a large number of samples are necessary for determining an EWMA-R control chart before using it.

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Online detection of the incidence via transfer learning

Yu,

Wang,

2024

Naval Research Logistics

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The counting process has abundant applications in reality, and Poisson process monitoring actually has received extensive attention and research. However, conventional methods experience poor performance when shifts appears early and only small number of historical observations in Phase I can be used for estimation. To overcome it, we creatively propose a new online monitoring algorithm under the transfer learning framework, which utilizes the information from observations of additional data sources so that the target process can be described better. By making the utmost of the somewhat correlated data from other domains, which is measured by a bivariate Gamma distributed statistic presented by us, the explicit properties (e.g., posterior probability mass function, posterior expectation, and posterior variance) are also strictly proved. Furthermore, based on the above theoretical results, we design two computationally efficient control schemes in Phase II, that is a control chart based on the cumulative distribution function for large shifts and an exponentially weighted moving average control chart for small shifts. For a better understanding of the more practical applications and transferability matter, we provide some optimal values for parameter setting. Extensive numerical simulations and a case of skin cancer incidence in America verify the superiorities of our approach.

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Shewhart control chart for monitoring the mean of Poisson mixed integer autoregressive processes via Monte Carlo simulation

Cited by 13 publications

References 37 publications

Monitoring the Zero-Inflated Time Series Model of Counts with Random Coefficient

Monitoring the Zero-Inflated Time Series Model of Counts with Random Coefficient

On autoregressive model selection for the exponentially weighted moving average control chart of residuals in monitoring the mean of autocorrelated processes

Online detection of the incidence via transfer learning

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