Shewhart Control Charts in New Perspective

Abstract The effects of estimating parameters and the violation of the assumption of normality when dealing with control charts are discussed. Corrections for estimating errors and extensions of the normal control chart to parametric and nonparametric charts are investigated. The underlying theory is extensively discussed, including the choice of a suitable parametric family containing the normal family. It turns out that classical contamination families like random or deterministic mixtures do not give a suitable solution here. The so-called normal power family leads to an acceptable family, as it is intimately connected to the problem at hand of modeling and estimating an extreme quantile. When the underlying distribution cannot be modeled sufficiently accurately by the normal power family, the nonparametric control chart comes into the picture. A data-driven procedure makes the choice between the three different charts. When the nonparametric chart turns up, a large number of Phase I observations are needed. When such a large sample size is not available, it may be preferred to replace the individual chart by a grouped one. The new minimum chart is recommended in that case.