Summary: Metrika (2009) 70:111130
Willem Albers · Wilbert C. M. Kallenberg
Received: 2 July 2007 / Published online: 26 March 2008
© The Author(s) 2008
Abstract Classical control charts are very sensitive to deviations from normality.
In this respect, nonparametric charts form an attractive alternative. However, these
often require considerably more Phase I observations than are available in practice.
This latter problem can be solved by introducing grouping during Phase II. Then each
group minimum is compared to a suitable upper limit (in the two-sided case also each
group maximum to a lower limit). In the present paper it is demonstrated that such
MIN charts allow further improvement by adopting a sequential approach. Once a
new observation fails to exceed the upper limit, its group is aborted and a new one
starts right away. The resulting CUMIN chart is easy to understand and implement.
Moreover, this chart is truly nonparametric and has good detection properties. For
example, like the CUSUM chart, it is markedly better than a Shewhart X-chart, unless
the shift is really large.
Keywords Statistical process control · Phase II control limits · Order statistics ·