Memorandum 1713

Self adapting control charts

W. Albers & W.C.M. Kallenberg

Abstract:
When the distributional form of the observations differs from normality, standard control charts are often seriously in error. Such model errors can be avoided with (modified) nonparametric control charts. Unfortunately, these control charts suffer from large stochastic errors due to estimation. In between are so called parametric control charts. All three of them are discussed in this paper as well as a combined chart, which chooses one of the three control charts according to the appropriate model assumption on the underlying distribution. The data themselves tell us which of the three control charts to select. Ready-made formulas for the several control charts are presented accompanied by an application on real data. Apart from bias removal, criteria based on exceedance probability and semi-variance are investigated.

Keywords:   Statistical process control, Phase II control limits, unbiasedness, exceedance probability, semi-variance, normal power family, model error, nonparametric, model selection

Mathematics Subject Classification:   62G32, 62P30, 65C05

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