Explicit Formulas of ARL on Double Moving Average Control Chart for Monitoring Process Mean of ZIPINAR(1) Model with an Excessive Number of Zeros
Abstract
Usually, the performance of control charts are widely measured by average run length (ARL). In this paper, the derivative explicit formulas of the ARL for double moving average (DMA) control chart are proposed for monitoring the process mean of zero-inflated Poisson integer-valued autoregressive first-order (ZIPINAR(1)) model. This model is fit when there are an excessive number of zeros in the count data. The performance of the DMA control chart is compared with the results of moving average and Shewhart control charts by considering from out of control average run length (ARL1). The numerical results found that the DMA control chart performed better than other control charts in order to detect mean shift in the process. In addition, the real-world application of the DMA control chart for ZIPINAR(1) process is addressed.
Keywords
[1] C. H. Sim and M. H. Lim, “Attribute charts for zero-inflated process,” Communications in Statistics-Simulation and Computation, vol. 37, pp. 1440–1452, 2008.
[2] M. Xie, B. He, and T. N. Goh, “Zero-inflated Poisson model in statistical process control,” Computational Statistics and Data Analysis, vol. 38, pp. 191–201, 2001.
[3] M. J. Campbell, D. Machin, and C. D'Arcangues, “Coping with extra-Poisson variability in the analysis of factors influencing vaginal ring expulsions,” Statistics in Medicine, vol. 10, pp. 241–251, 1991.
[4] D. A. Freund, T. J. Kniesner, and A. T. LoSasso, “Dealing with the common econometric problems of count data with excess zeros endogenous treatment effects and attrition bias,” Economics Letters, vol. 62, p. 62, 1999.
[5] M. A. AI-Osh and A. A. Alzaid, “First-order integer-valued autoregressive (INAR(1)) process,” Journal of Time Series Analysis, vol. 8, pp. 261– 275, 1987.
[6] V. Shankar, J, Milton, and F. Mannering, “Modeling accident frequencies as zero-altered probability processes: An empirical inquiry,” Accident Analysis and Prevention, vol. 29, pp. 829–837, 1997.
[7] S. P. Miaou, “The relationship between truck accidents and geometric design of road sections Poisson versus negative binomial regressions,” Accident Analysis and Prevention, vol. 26, pp. 471– 482, 1994.
[8] M. A. Jazi, G. Jones, and C. D. Lai, “First‐order integer-valued AR processes with zero-inflated Poisson innovations,” Journal of Time Series Analysis, vol. 33, pp. 954–963, 2012.
[9] M. Cardinal, R. Roy, and J. Lambert, “On the application of integer-valued time series models for the analysis of disease incidence,” Statistics in Medicine, vol.18, pp. 2025–2039, 1999.
[10] E. S. Page, “Continuous inspection schemes,” Biometrika, vol. 41, pp. 100–144, 1954.
[11] S. W. Roberts, “Control chart tests based on geometric moving average,” Technometrics, vol. 1, pp. 239– 250, 1959.
[12] M. B. C. Khoo, “A moving average control chart for monitoring the fraction nonconforming,” Quality and Reliability Engineering International, vol.20, pp. 617–635, 2004.
[13] M. B. C. Khoo and V. H. Wong, “A double moving average control chart,” Communication in Statistics – Simulation and Computation, vol. 37, pp. 1696–1708, 2008.
[14] S. Knoth, “Accurate ARL calculation for EWMA control charts monitoring normal mean and variance simultaneously,” Sequential Analysis, vol. 26, pp. 251–263, 2006.
[15] C. M. Borror, D. C. Montgomery, and G. C. Runger, “Robustness of the EWMA control chart to non-normality,” Journal of Quality Technology, vol. 31, pp. 309–316, 1999.
[16] S. Sukparungsee, “Average run length of Cumulative Sum control chart by Markov chain approach for zero-inflated Poisson processes,” Thailand Statistician, vol. 16, pp. 6–13, 2018.
[17] S. V. Crowder, “A simple method for studying runlength distributions of exponentially weighted moving average charts,” Technometrics, vol. 29, pp. 401–407, 1978.
[18] W. Peerajit, Y. Areepong, and S. Sukparungsee, “Analytical explicit formulas of average run length of long memory process with ARFIMA model on CUSUM control chart,” Songklanakarin Journal of Science and Technology, vol. 39, pp. 779–786, 2017.
[19] S. Suriyakat, “Performance of EWMA chart for trend autoregressive model with exponential white noise,” Silpakorn University Science and Technology Journal, vol. 11, pp. 16–22, 2017.
[20] Y. Areepong, “Explicit formulas of average run length for a moving average control chart for monitoring the number of a defective product,” International Journal of Pure and Applied Mathematics, vol. 3, pp. 331–343, 2012.
[21] Y. Areepong and S. Sukparungsee, “The closed-form formulas of average run length of moving average control chart for nonconforming for zero-inflated process,” Far East Journal of Mathematical Sciences, vol. 75, pp. 385–400, 2013.
[22] C. Chananet, Y. Areepong, and S. Sukparungsee, “An approximate formula for ARL in moving average chart with ZINB data,” Thailand Statistician, vol. 13, pp. 209–222 2015.
[23] A. C. Rakitzis, C. H. Weiβ, and P. Castagliola, “Control charts for monitoring correlated poisson counts with an excessive number of zeros,” Quality and Reliability Engineering International, vol. 33, pp. 413–430, 2017.
[24] Y. Areepong, “Moving average control chart for monitoring process mean in INAR(1) process with zero-inflated Poisson,” International Journal of Science and Technology, vol. 4, pp. 138–149, 2018.
[25] Mathematica, Mathematica Version 12.2, 2020.
DOI: 10.14416/j.asep.2021.03.002
Refbacks
- There are currently no refbacks.
.png){kind=logo}
