Improved Distribution-free Control Chart for the Joint Monitoring of Location and Scale

The nonparametric (distribution-free) Shewhart-type control chart based on the Pettitt test has recently been introduced in the literature for joint monitoring of the location and the scale parameters of a continuous process. The chart is based on a simple random sampling (SRS) technique (denoted as SP-SRS chart). In the literature, the ranked set sampling (RSS) technique is preferred over the SRS technique as it reduces the variability and improves the performance of the control chart. The aim of this paper is to develop a distribution-free control chart based on the Pettitt test using the RSS technique (denoted as SP-RSS Chart) further to enhance the joint monitoring of location and scale. The run length performance of the proposed SP-RSS chart is compared with the SP-SRS chart. The comparison revealed that the proposed SP-RSS chart outperforms the SP-RSS chart for joint monitoring of the location and scale of a continuous process.