On the Occurrence of<i>n</i>Successes Within<i>N</i>Bernoulli Trials

Abstract

Several zone tests for quality-control charts are considered. One test calls for initiating a search for an assignable cause whenever n out of N consecutive points fall in some predetermined warning zone. An algorithm is given for obtaining the average-run-length of this procedure; and several alternative procedures, for which the average-run-lengths are explicitly given, are suggested. Also, a simple means is given for finding the average-run-length of procedures that combine a zone test with the standard 3σ-limit.