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Summary.  A class of Shewhart‐type distribution‐free control charts is considered. A key advantage of these charts is that the in‐control run length distribution is the same for all continuous process distributions. Exact expressions for the run length distribution and the average run length (ARL) are derived and properties of the charts are studied via evaluations of the run length distribution probabilities and the ARL. Tables are provided for implementation for some typical ARL values and false alarm rates. The charts proposed are preferable from a robustness point of view, have attractive ARL properties and would be particularly useful in situations where one uses a classical Shewhart  X‐chart. A numerical illustration is given.

Summary  In this paper the concept of ‘rank‐interaction’ is introduced and a distribution‐free method for testing against the presence of ‘rank‐interaction’ is suggested in the case of a two‐way layout (classification) with m (> 1) observations per cell. Roughly speaking rank‐interaction can be understood as the phenomenon at which the ranks of the levels of some relevant variable are different for different classes of the other factor. The exact null distribution of the test statistic has been computed in some cases. The asymptotic distribution under the null hypothesis has been derived. A test suggested by J.V. Bradleyin his book ‘Distribution‐free Statistical Tests’ [2] is discussed. In the opinion of the authors it is doubtful whether the asymptotic distribution of the test statistic under the null hypothesis, as given by Bradley, is correct. The test of Bradleywas intended to be sensitive to the presence of interactions defined in the usual way and hence not only to ‘rank‐interaction’. The same applies to methods proposed by some other authors. We claim that situations exist where one should test against rank‐interaction and not against the usual more general alternative.

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