ENBIS: European Network for Business and Industrial Statistics

Group Inspection of Dependent Binary Processes

22 September 2008, 14:00 – 14:20

Abstract

Submitted by

Christian Weiß

Authors

Christian H. Weiß

Affiliation

University of Würzburg

Abstract

The statistical control of attribute data processes is an area of emerging interest both in research and professional practice. Often one is concerned with binary attribute processes. Such binary quality characteristics may describe the result of an inspection of an item: A nonconformity is a non-fulfillment of a requirement in general, while a defect can be considered as a serious nonconformity, as a non-fulfillment of a requirement related to an intended or specified use (DIN EN ISO 9000, 2005, p. 27). In practice, it is often impossible to monitor the process continuously: The evaluation of the items may be too expensive or perhaps even destroy the items, the evaluation takes too much time (at least relative to the process speed), or it may be quite complex (e. g., endurance or tolerance tests). If the process cannot be monitored continuously, then one can analyze connected segments instead, where two successive segments have a sufficiently large time-lag such that they can be assumed to be approximately independent of each other. Nevertheless, the serial dependence has to be considered at least within the segments, i. e., the distribution of the segment sums is not binomial anymore.

We propose the Markov binomial distribution to approximate the true distribution of the segment sums. Based on this distribution, we develop a Markov np chart and a Markov EWMA chart. We show how average run lengths (ARL) can be computed exactly for both types of chart. Based on such ARL computations, we derive recommendations for chart design and investigate the out-of-control performance. A real-data example of counts of web accesses illustrates the application of these charts in practice.

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