A New Nonparametric Control Chart For The Joint Monitoring Of Location And Scale Using Ranked Set Sampling

Abstract

Control charts are frequently employed in the field of statistical process monitoring (SPM) to track both the average and variability of a process. In this study, a novel nonparametric control chart is introduced, which utilizes modified Lepage-type test.

This proposed chart serves the purpose of concurrently monitoring both location and scale parameters for any continuous distribution related to a specific process. The charting statistic combines two well-known nonparametric test statistics: Baumgartner's test for location and Ansari-Bradley's test for scale estimation.

The performance of the proposed chart is evaluated in simulation studies, focusing on statistical metrics such as mean, standard deviation, median and various percentiles that characterize the distribution of run lengths. The behaviour of the chart under both in-control and out-of-control conditions is examined through simulation studies using two sampling methods: simple random sampling (SRS) and ranked set sampling (RSS).