Nonparametric Shewhart-Type Sign Control Charts Based on Runs

Abstract

Nonparametric control charts are considered for the median and other percentiles based on runs of sign statistics above and below the control limits. It is noted that the sign charts are advantageous in certain practical situations. Expressions for the run-length distributions are derived using Markov chain theory; several examples are given. The in-control (IC) and the out-of-control (OOC) performance of these charts are studied and compared to the existing nonparametric Wilcoxon signed-ranked charts of Chakraborti and Eryilmaz (2007 Chakraborti , S. , Eryilmaz , S. ( 2007 ). A nonparametric Shewhart-type signed-rank control chart based on runs . Commun. Statist. Simul. Computat. 36 ( 2 ): 335 – 356 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) under the normal, the double exponential and the Cauchy distributions, using the average run-length (ARL), the standard deviation of the run-length (SDRL), the false alarm rate (FAR) and some percentiles of the run-length, including the median run-length (MDRL). It is shown that the proposed “runs-rules enhanced” sign charts offer more practically desirable IC ARL (ARL 0) and FAR values and perform better for some heavy-tailed distributions. Some concluding remarks are offered.