Parametric Control Charts

Standard control charts are based on the assumption that the observations are normally distributed. 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 larger parametric models, with emphasis on 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. Keyword and phrases: statistical process control, Phase II control limits, second order unbiasedness, normal power family, model error, stochastic error. 2000 Mathematics Subject Classification: 62 F 12, 62 P 30, 65 C 05. This research was supported by the Technology Foundation STW, applied science division of NWO and the technology programme of the Ministry of Economic Affairs.