Control charts for location based on different sampling schemes

Abstract

Control charts are the most important statistical process control tool for monitoring variations in a process. A number of articles are available in the literature for the X̄ control chart based on simple random sampling, ranked set sampling, median-ranked set sampling (MRSS), extreme-ranked set sampling, double-ranked set sampling, double median-ranked set sampling and median double-ranked set sampling. In this study, we highlight some limitations of the existing ranked set charting structures. Besides, we propose different runs rules-based control charting structures under a variety of sampling strategies. We evaluate the performance of the control charting structures using power curves as a performance criterion. We observe that the proposed merger of varying runs rules schemes with different sampling strategies improve significantly the detection ability of location control charting structures. More specifically, the MRSS performs the best under both single- and double-ranked set strategies with varying runs rules schemes. We also include a real-life example to explain the proposal and highlight its significance for practical data sets.

Keywords:

• control charts
• power
• runs rules
• sampling strategies
• statistical process control

Acknowledgements

The authors are greatly thankful to the anonymous reviewers and the editor for their encouragement and valuable suggestions to further improve the initial version of the article. The author Muhammad Riaz is indebted to the King Fahd University of Petroleum and Minerals, Saudi Arabia for providing excellent research facilities under IN111059. The authors are also thankful to Soil and Water Testing Laboratory R.Y.K, Pakistan for their co-operation about EC example data.