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The influence of the estimation of parameters in Shewhart control charts is investigated. It is shown by simulation and asymptotics that (very) large sample sizes are needed to accurately determine control charts if estimators are plugged in. Correction terms are developed to get accurate control limits for common sample sizes in the in-control situation. Simulation and theory show that the new corrections work very well. The performance of the corrected control charts in the out-of-control situation is studied as well. It turns out that the correction terms do not disturb the behavior of the control charts in the out-of-control situation. On the contrary, for moderate sample sizes the corrected control charts remain powerful and therefore, the recommendation to take at least 300 observations can be reduced to 40 observations when corrected control charts are applied. Copyright Springer-Verlag 2004Statistical process control; Phase II control limits; second order unbiasedness; out-of-control, 62F12, 62P30,

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In recent years several authors have recommended smooth tests for testing goodness of fit. However, the number of components in the smooth test statistic should be chosen well; otherwise, considerable loss of power may occur. Schwarz's selection rule provides one such good choice. Earlier results on simple null hypotheses are extended here to composite hypotheses, which tend to be of more practical interest. For general composite hypotheses, consistency of the data-driven smooth tests holds at essentially any alternative. Monte Carlo experiments on testing exponentiality and normality show that the data-driven version of Neyman's test compares well to other, even specialized, tests over a wide range of alternatives.