Joint Research Conference
June 24-26, 2014
EWMA Control Charts Monitoring Normal Variance When No Standard is GivenMost of the literature concerned with the design of control charts relies on perfect knowledge of the distribution for at least the in-control process. Some papers treated the handling of EWMA charts monitoring normal mean in case of unknown parameters -- refer to Jones et al. (2001). In Jensen et al. (2006), ``Effects of Parameter Estimation on Control Chart Properties: A Literature Review'' and more recently in Psarakis et al. (2013), ``Some Recent Developments on the Effects of Parameter Estimation on Control Charts'' some reviews were published. In Jensen et al. (2006), it was mentioned that it would be useful to evaluate and take into account these effects also for variance control charts. Here, we consider EWMA charts for monitoring the normal variance. First results on EWMA charts for normal variance, based on log S^2, are given in Maravelakis and Castagliola (2009). However, they focus on providing recommendations for the choice of the size of the phase I sample and for the smoothing constant of the EWMA iteration. This is the most popular analysis framework. Here, a different way of adapting the uncertainty of phase I estimates is treated: Setup the chart through specifying a certain false alarm probability such as, e. g., the probability to get a false alarm within a typical monitoring horizon, say 1000 observations, is not larger than alpha. This results in a specific alarm threshold. Here we describe a feasible way to determine this threshold in case of unknown parameters for a phase I series of given size (and structure). We study upper and two-sided version of EWMA charts based on the sample variance S^2.