An Evaluation of Average Run Length of MaxEWMA and MaxGWMA Control Charts

Exponentially weighted moving average control chart (EWMA) is a popular chart used for detecting shift in the mean of parameter of distributions in quality control. The objective of this paper is to compare the efficiency of control chart to detect an increases in the mean of a process. In particular, we compared the Maximum Exponentially Weighted Moving Average (MaxEWMA) and Maximum Generally Weighted Moving Average (MaxGWMA) control charts when the observations are Exponential distribution. The criteria for evaluate the performance of control chart is called, the Average Run Length (ARL). The result of comparison show that in the case of process is small sample size, the MaxEWMA control chart is more efficiency to detect shift in the process mean than MaxGWMA control chart. For the case of large sample size, the MaxEWMA control chart is more sensitive to detect small shift in the process mean than MaxGWMA control chart, and when the process is a large shift in mean, the MaxGWMA control chart is more sensitive to detect mean shift than MaxEWMA control chart.

• S. Phanyaem

• Maximum Exponentially Weighted Moving Average
• Maximum General Weighted Moving Average
• Average Run Length.

<p>[1] D.M. Hawkins and D.H. Olwell, &ldquo;Cumulative Sum Charts and Charting for Quality Improvement,&rdquo; 1998, Springer, New York. [2] E.S. Page, &ldquo;Continuous inspection schemes,&rdquo; Biometrika 41, 1995, pp. 100-115. [3] E. Yashchin, &ldquo;Statistical control schemes: Methods, Applications and generalization,&rdquo; International Statistical 61, 1993, pp. 41-66. [4] E. Yashchin, &ldquo;Performance of CUSUM control schemes for serially correlated observations,&rdquo; Technometrics 35, 1993, pp. 37-52. [5] G. Chen, S. W. Cheng, and H. Xie, &ldquo;Monitoring process mean and variability with one EWMA chart,&rdquo; Journal of Quality Technology 33, 2001, pp. 223-233. [6] H. Xie, &ldquo;Contributions to qualimetry,&rdquo; Ph.D. Thesis. Winnipeg, Canada: University of Manitoba, pp. 23-37. [7] J.M. Lucas and M.S. Saccucci, &ldquo;Exponentially weighted moving average control schemes: properties and enhancements,&rdquo; Technometrics 32, 1990, pp. 1-29. [8] M.S. Srivastava and Y.H. Wu, &ldquo;Comparison of EWMA, CUSUM and Shiryayev-Roberts procedures for detecting a shift in the mean,&rdquo; The Annals of Statistics 21, 1993, pp. 645-670. [9] M.S. Srivastava and Y.H. Wu, &ldquo;Evaluation of optimum weights and average run lengths in EWMA control schemes,&rdquo; Communications in Statistics: Theory and Methods 26, 1997, pp.1253-1267. [10] S.W. Roberts, &ldquo;Control chart tests based on geometric moving average,&rdquo; Technometrics 1, 1959, pp. 239-250. [11] S. Sheu, C. Huang and T. Hsu, &ldquo;Extended maximum generally weighted moving average control chart for monitoring process mean and variability,&rdquo; Computers &amp; Industrial Engineering 62, 2012, pp. 216-225. [12] Y.H. Wu, &ldquo;Design of control charts for detecting the change point, In Change-Point Problems,&rdquo; 1994, pp. 330-345.</p>