The Detection of Shifts in the Ratio of Two Poisson Means with an Exponentially Weighted Moving Average Control Chart
Keywords:
Exponentially weighted moving average, Cumulative Sum, average run lengthAbstract
The Exponentially Weighted Moving Average (EWMA) control chart is widely used for detecting and controlling the variations in production processes in order to gain efficient manufacturing process. The control chart can be applied to engineering, medical, financial, psychology fields, and etc. In general, one of the control chart performance metrics is Average Run Length (ARL). Therefore, the objective for this research is to approximate the ARL using Markov Chain Approach (MCA) for EWMA control charts for a binomial distribution underlying the ratio of two Poisson means. The proposed MCA is compared with Monte Carlo Simulation (MC) by using absolute percentage relative error. In addition, this research compared the efficiency of EWMA and Cumulative Sum (CUSUM) control charts and found that in the aspect of process change detection, CUSUM performed better than EWMA for all changing levels.
References
Brook, D., & Evans, D. A. (1972). An approach to the probability distribution of Cusum run length. Biometrika, 59, 539-548.
Bratcher, T. L., & Stamey, J. D. (2004). A note on Bayesian interval estimators for comparing two Poisson rates. TheMathematical Scientist, 29, 54-60.
Chen, N., Zhou, S., Chang, T-S., & Huang, H. (2008). Attribute control charts using generalized zero-inflated Poisson distribution. Quality and Reliability Engineering International, 24, 793-806.
Gan, F. F. (1990). Monitoring observations generated from a binomial distribution using modified exponentially weighted moving average control chart. Journal of Statistical Computation and Simulation, 37, 45-60.
Gu, X., Ng, H. K. T., Tang, M. L., & Schucany, W. R. (2008). Testing the ratio of two Poisson rates. Biometrical Journal, 50, 283-298.
Hoffman, D. (2003). Negative binomial control limits for counted data with extra-Poisson variation. Pharmaceutical Statistics, 2, 127-132.
Han, D., Tsung, F., Li, Y., & Xian, J. (2010). Detection of changes in a random financial sequence with a stable distribution. Journal of Applied Statistics, 37, 1089–1111.
Krishnamoorthy, K., & Thomson, J. (2004). A more powerful test for comparing two Poisson means. Journal of Statistical Planning and Inference, 119, 23-35.
Lucas, J. M. (1985). Counted data CUSUM’s. Technometrics, 27, 29-44.
Lucas, J. M., & Saccucci, M. S. (1990). Exponentially weighted moving average control schemes: properties and enhancements. Technometrics, 32, 1-29.
Nelson, L. S. (1987). Comparison of Poisson means: The general Case. Journal of Quality Technology, 19, 173-179.
Nong, Y., Connie, B., & Yebin, Z. (2002). EWMA techniques for computer intrusion detection through anomalous changes in event intensity. Quality and Reliability Engineering International, 18, 443-451.
Price, R. M., & Bonett, D. G. (2000). Estimating the ratio of two Poisson rates. Computational Statistics and Data Analysis, 34, 345-356.
Roberts, S. W. (1959). Control chart tests based on geometric moving average. Technometrics, 1, 239-250.
Shewhart, W. A. (1931). Economic Control of Quality of Manufactured Product. New York: D. Van Nostrand Company.
Sahai, H., & Misra, S. C. (1992). Comparing means of two Poisson distributions. The Mathematical Scientist, 17, 60-67.
Zhang, L., & Chen, G. (2004). EWMA Charts for monitoring the mean of censored Weibull lifetimes. Journal of Quality Technology, 36, 321-328.
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