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Negative Binomial charts for monitoring high-quality processes

Summary: Negative Binomial charts for monitoring
high-quality processes
Willem Albers
Department of Applied Mathematics
University of Twente
P.O. Box 217, 7500 AE Enschede
The Netherlands
Abstract. Good control charts for high quality processes are often based on the number of successes between
failures. Geometric charts are simplest in this respect, but slow in recognizing moderately increased failure rates p.
Improvement can be achieved by waiting until r > 1 failures have occurred, i.e. by using negative binomial charts.
In this paper we analyze such charts in some detail. On the basis of a fair comparison, we demonstrate how the
optimal r is related to the degree of increase of p. As in practice p will usually be unknown, we also analyze the
estimated version of the charts. In particular, simple corrections are derived to control the non-negligible effects of
this estimation step.
Keywords and phrases: Statistical Process Control, health care monitoring, geometric charts, average run length,
estimated parameters
2000 Mathematics Subject Classification: 62P10, 62C05, 62F12
1 Introduction and motivation
For decades a lot of effort has been devoted to improving quality in production. As a result,
nowadays we are often dealing with high-quality industrial processes in which the proportion of


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


Collections: Engineering