### Explicit Formulas of Moving Average Control Chart for Zero Modified Geometric Integer Valued Auto Regressive Process

#### Abstract

#### Keywords

[1] W. Barreto-Souza, “Zero-modified geometric INAR(1) process for modeling count time series with deflation and inflation zeros,” *Journal of Time Series Analysis*, vol. 36, no. 6, pp. 839–852, 2015, doi: 10.1111/jtsa.12131.

[2] W. A. Shewhart, Economic Control Chart of Quality of Manufactured Product,” *New York: D. Van Nostrand Company*, pp. 115–179, 1931.

[3] M. B. C. Khoo, “A moving average control chart for monitoring the fraction non-conforming,” *Quality and Reliability Engineering International*, vol. 20, pp. 617–635, 2004, doi: 10.1002/qre.576.

[4] D. C. Montgomery, *Statistical Quality Control*. 6th ed. New York: John Wiley&Sons, 2008, pp. 72–150.

[5] D. Brook and D. A. Evans, “An approach to the probability distribution of CUSUM run length,” *Biometrika*, vol. 59, no. 3, pp. 539–549, 1972, doi: 10.2307/2334805.

[6] S. V. Crowder, “A simple method for studying run length distribution of exponential weight moving average control charts,” *Technometrics*, vol. 29, no. 4, pp. 401–407, 1987, doi: 10.2307/1269450.

[7] A. C. Rakitzis, P. Castagliola, and P. E. Maravelakis, “Cumulative sum control charts for monitoring geometrically inflated Poisson processes: An application to infectious disease counts data,” *Statistical Methods in Medical Research*, vol. 1, no. 1, pp. 1–19, 2016, doi: 10.1177/ 0962280216641985.

[8] A. C. Rakitzia, P. E. Maravelakis, and P. Castagliola, “CUSUM control charts for the monitoring of zero-inflated Binomial processes,” *Quality and Reliability Engineering International*, vol. 32, no. 2, pp. 413–430, 2016, doi: 10.1002/qre.1764.

[9] A. C. Rakitzis, C. H. Weiβ, and P. Castagliola, “Control charts for monitoring correlated counts with a finite range,” *Applied Stochastic Models in Business and Industry*, vol. 49, no. 3, pp. 553–573, 2022, doi: 10.1080/02664763.2020.1820959.

[10] S. Sukparungsee, “Average run length of cumulative sum control chart by Markov chain approach for zero-inflated Poisson process,” *Thailand Statistician*, vol. 16, no. 1, pp. 6–13, 2018,

[11] S. Phanyam, “The Integral equation approach for solving the average run length of EWMA process for autocorrelated process,” *Thailand Statistician*, vol. 19, no. 3, pp. 627–641. 2021.

[12] Y. Areepon and S. Sukparungsee, “An integral equation approach to EWMA chart for detecting a change in lognormal distribution,” *Thailand Statistician*, vol. 8, no. 1, pp. 47–61, 2010.

[13] C. Chananet, Y. Areepong, and S. Sukparungsee, “On designing a moving average-range control chart for enhancing a process variation detection,” *Applied Science and Engineering Progress*, vol. 17, no. 1, 2024, Art. no. 6882, doi: 10.14416/j.asep. 2023.06.001

[14] Y. Areepong and S. Sukparungsee, “The closed-form formulas of average run length of moving average control chart for non-conforming for zero-inflated process,” *Far East Journal of Mathematical Sciences*, vol. 75, pp. 385–400, 2013.

[15] C. Chananet, Y. Areepong, and S. Sukparungsee, “An approximate formula for ARL in moving average chart with ZINB data,” *Thailand Statistician*, vol. 13, no. 2, pp. 209–222, 2015.

[16] S. Phantu, S. Sukparungsee, and Y. Areepong, “Explicit expressions of average run length of moving average control chart for Poisson integer-valued autoregressive model,” in *Proceeding of the International Multiconference of Engineers and Computer Scientists*, vol. 2, pp. 1–4, 2016.

[17] S. Sukparungsee, S. Phantu, and Y. Areepong, “Explicit formula of average run length of moving average control chart for Poisson INMA(1) process,” *Advances and Applications in Statistics*, vol. 52, no. 4, pp. 235–250, 2018, doi: 10.17654/as052040235.

[18] 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, no. 3, pp. 138–149, 2018, doi: 10.20319/mijst. 2018.43.138149.

[19] K. Raweesawat and S. Sukparungsee, “Explicit formula of ARL on double moving average control chart for monitoring process mean of ZIPINAR(1) model with an Excessive number of zeros,” *Applied Science and Engineering Progress*, vol. 15, no. 3, 2022, Art. no. 4588, doi : 10.14416/j.asep.2021.03.002.

[20] S. Wiwek and S. Sukparungsee, “Explicit formulas of average run length for mixed moving average-exponentially weighted moving average control chart,” *The Journal of KMUTNB*, vol. 33, no. 2, pp. 613–625, 2023, doi: 10.14416/j.kmutnb. 2022.06.005.

[21] E. McKenzie, “Some simple model for discrete variable time series,” *Journal of the American Water Resources Association (JAWRA)*, vol. 21, no. 4, pp. 645–650, 1985, doi: 10.1111/j.1752 1688.1985.tb05379.x.

[22] M. A. Al-Osh and A. A. Alzaid, “First-order integer-valued autoregressive (INAR(1)) process,” *Journal of Time Series Analysis*, vol. 8, no. 3, pp. 261–275, 1987, doi: 10.1111/j.1467-9892.1987. tb00438.x.

[23] M. Bourguinon and C. H. Weiβ, “An INAR(1) process for modeling count time series with equidispersion, underdispersion and overdispersion,” *Test*, vol. 26, no. 4, pp. 847–868, 2017.

[24] A. C. Rakitzis, C. H. Weiβ, and P. Castagliola, “Control charts for monitoring correlated Poisson counts with excessive zeros,” *Quality and Reliability Engineering International*, vol. 33, no. 2, pp. 416–430, 2016.

[25] *Mathematica*, Mathematica Version 6.0, 2012.

DOI: 10.14416/j.asep.2023.09.004

### Refbacks

- There are currently no refbacks.