MIXMAX charts

For attribute data with (very) small failure rates control charts based on subsequent groups of r failure times, for some r >= 1, have been shown to be attractive. This especially holds for charts which stop once the maximum (MAX) of such a group is sufficiently small, as this choice allows a nonparametric adaptation already for Phase I samples of ordinary size. The choice of r is dictated by the suspected rate of change in failure rate once the process goes out-of-control: for large (small) changes, r should be small (large). Typically,the actual rate of change will be unknown and hence some flexibility w.r.t. the choice of r seems advisable. In the present paper this goal is achieved by mixing a MAX-chart for a large r with one for which r is relatively small.