A Study of the Performance of EWMA Chart with Transformed Weibull Observations

  • Saowanit Sukparungsee Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand.
  • Yupaporn Areepong Department of Mathematical Sciences, Faculty of Science, University of Technology, Sydney NSW, 2007, Australia.
Keywords: averaged run length and average delay, cumulative sum, exponentially weighted moving average chart, stopping times


Statistical Process Control (SPC) chart for detecting small shifts in parameter of distributions are widely used in quality control and other area of applications is an Exponentially Weighted Moving Average (EWMA) procedure. The objective of this paper is to implement an explicit formula for characteristics of EWMA as Average Run Length (ARL) – the expectation of false alarm times and Average Delay time (AD) – the expectation of delay of true alarm times in case of Weibull distribution. Using the simple transformation technique, we obtain the explicit expressions for evaluating ARL and AD when observations are Weibull by taking power of such observations. The accuracy of results is compared with Monte Carlo simulations. In addition, we present the table of optimal parameter values for Weibull EWMA designs and the comparisons of performance of EWMA versus CUSUM charts are considered.