A Nonparametric Control Chart for Location Based on Sub-Samples of Size Two

Abstract

Control charts are widely used in statistical process control to detect changes in a production process and for monitoring a process to make sure that it is in control. In conventional statistical process control, the pattern of chance causes is often assumed to follow normal distribution. It is well known that the assumption of normality or any specific parametric form for the process distribution is too restrictive. In such situations, distribution-free or nonparametric control charts can serve the purpose better. In this paper, distribution-free control charts are developed based on a class of one-sample test statistics with sub-samples of size two due to Mehra, Prasad and Madhava Rao (Austral. J. Statist. 32: 373392, 1990). The control charts based on their statistic (-chart) are easy to understand and to use. The performance of the proposed procedures is studied through the average run length, which is the expected number of samples required by the procedure to signal out of control. It is observed that the performance of the proposed chart is better than the existing charts in the literature.