 
Summary: MIXMAX charts
Willem Albers
Department of Applied Mathematics
University of Twente
P.O. Box 217, 7500 AE Enschede
The Netherlands
Abstract. 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 outofcontrol: 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 MAXchart for a large r with one for which r is relatively
small.
Keywords and phrases: Statistical Process Control, health care monitoring, high quality processes, average run
length, estimated parameters, order statistics, sets method
2000 Mathematics Subject Classification: 62P10, 62C05, 62G15
1 Introduction and motivation
Highquality processes are increasingly common in industrial settings, as production stan
dards have steadily been improving over the last decades. Moreover, in the application area of
