On the Average Run Lengths of Quality Control Schemes Using a Numerical Integral Equation Approach
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Abstract
This research presents the approach of estimating the average run length (ARL) by using the numerical integral equation (NIE) approach, such as the Gaussian, Midpoint, Trapezoidal, and Simpson’s rules for the extended exponentially weighted moving average (EEWMA) control chart, when observations are continuous distributions namely exponential, Weibull and Gamma distributions. In addition, the performance of the extended exponentially weighted moving average (EEWMA) control chart is compared with the modified exponentially weighted moving average (modified EWMA) and exponentially weighted moving average (EWMA) control charts. The performance metric is the out-of-control average run length (ARL1). The results show that the EEWMA control chart performs the best among the modified EWMA and EWMA control charts. Furthermore, the efficacies of the control charts using the approximated ARL solutions were also applied to real-world applications.
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References
W. A. Shewhart, Economic Control of Quality of Manufactured Product. Connecticut: Martino Fine Books, 2015.
S. W. Robert, “Control chart test based on geometric moving average,” Technometrics, vol. 1, pp. 239– 250,1959.
A. K. Patel and J. Divecha, “Modified exponentially weighted moving average (EWMA) control chart for an analytical process data,” Journal of Chemical Engineering and Materials Science, vol. 2, no. 1, pp. 12–20, 2011.
N. Khan, M. Aslam, and C. Jun, “Design of a control chart using a modified EWMA statistic,” Quality and Reliability Engineering International, vol. 33, no. 5, pp. 100–114, 2017.
M. Naveed, M. Azam, N. Khan, and M. Aslam, “Design of a control chart using extended EWMA statistic,” Technologies, vol. 6, pp. 108–122, 2018.
C. W. Champ and S. E. Rigdon, “A comparison of the Markov chain and the integral equation approaches for evaluating the run length distribution of quality control charts,” Communications in Statistics - Simulation and Computation, vol. 20, no. 1, pp. 191–204, 1991.
Y. Areepong and R. Sunthornwat, “Controlling the velocity and kinetic energy of an ideal gas: An ewma control chart and its average run length analytical approximations for detection of a change-point in case of light-tailed distributions,” Walailak Journal of Science and Technology, vol. 18, no. 10, 2021, Art. no. 9586.
P. Phanthuna, Y. Areepong, and S. Sukparungsee, “Detection capability of the modified EWMA chart for the trend stationary AR(1) model,” Thailand Statician, vol. 19, no. 1, pp. 70–81, 2021.
W. Peerajit, Y. Areepong, and S. Sukparungsee, “Explicit analytical solutions for ARL of CUSUM chart for a long-memory SARFIMA model,” Communications in Statistics Part B: Simulation and Computation, vol. 48, pp. 1176– 1190, 2019.
S. Phanyaem, “Estimating the average run length of CUSUM control chart for seasonal autoregressive integrated moving average of order (P, D, Q)L model,” The Journal of Applied Science, vol. 19, no.2, pp. 52–60, 2020.
Y. Areepong and S. Sukparungsee, “An integral equation approach to EWMA chart for detecting a change in lognormal distribution,” Thailand Statician, vol. 8, no. 1, pp. 47–61, 2010.
P. Phanthuna and Y. Areepong, “Analytical solutions of arL for sar(p)l model on a modified ewma chart,” Mathematics and Statistics, vol. 9, pp. 685–696, 2021.
K. Karoon, Y. Areepong, and S. Sukparungsee, “Numerical integral equation methods of average run length on extended EWMA control chart for autoregressive process,” in Proceeding of WCE, 2021, pp. 51–56.
N. Antonio, A. D. Almeida, and L. Nunes, “Hotel booking demand datasets,” 2019. [Online]. Available: https://reader.elsevier.com/reader/sd/pii/
Transport and Main Roads Customer Service Centre, “Customer service centre wait time,” 2021. [Online]. Available: https://www.data. qld. gov.au/