Summary: Journal of Statistical Planning and
Inference 124 (2004) 159184
Parametric control charts
Willem Albers, Wilbert C.M. Kallenberg, Sri Nurdiati
Faculty of Mathematical Sciences, University of Twente, P.O. Box 217,
7500 AE Enschede, Netherlands
Received 6 June 2002; accepted 19 March 2003
Standard control charts are based on the assumption that the observations are normally dis-
tributed. In practice, normality often fails and consequently the false alarm rate is seriously in
error. Application of a nonparametric approach is only possible with many Phase I observations.
Since nowadays such very large sample sizes are usually not available, there is need for an
intermediate approach by considering a larger parametric model containing the normal family
as a submodel. In this paper control limits are presented in such a larger parametric model,
the so called normal power family. Correction terms are derived, taking into account that the
parameters are estimated. Simulation results show that the control limits are accurate, not only
in the considered parametric family, but also for common distributions outside the parametric
family, thus covering a broad class of distributions.
c 2003 Elsevier B.V. All rights reserved.