False Signal Rates for the Shewhart Control Chart with Supplementary Runs Tests

Abstract

It is common practice to supplement the Shewhart X̄ chart with so called “runs tests.” These tests are designed to give an earlier detection of anomalies in the process mean. Although these tests are valuable in detecting “true” problems, they also increase the probability of a false signal. In this paper the false signal rates of eight runs tests are obtained through simulation. In-control processes were generated using independent realizations of a standard normal distribution. The results show that the number of false signals can be fairly high, particularly when the number of tests applied and number of subgroups increase.