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Control charts for high-quality processes: MAX or CUMAX ?

Summary: Control charts for high-quality processes:
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 were introduced which are based
on subsequent groups of r failure times, for some r 1. Within this family, it was shown to be attractive
to stop once the maximum of such a group is sufficiently small, because this choice allows a very satisfactory
nonparametric adaptation. The question we address here is whether a cumulative approach offers even further
improvement. Thus instead of fixed groups, we shall use the first sequence of r consecutive sufficiently small
failure times to produce a signal. A further reason for considering this type of chart is the fact that it forms
the nonparametric counterpart of the well-known sets method.
Keywords and phrases: Statistical Process Control, health care monitoring, geometric charts, average run length,
estimated parameters, order statistics, sets method
2000 Mathematics Subject Classification: 62P10, 62C05, 62G15
1 Introduction and motivation
By virtue of ever increasing standards, high-quality processes are more and more common in
industrial settings. Moreover, for health care monitoring they even form the standard, as in


Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente


Collections: Engineering