On the performance of X̄ control chart for known and unknown parameters supplemented with runs rules under different probability distributions

ABSTRACT

In this study two design structures of $\overline{X}$ control chart are proposed for known and unknown process parameters, under the variety of runs rules and process distributions. The proposed structures are developed by taking into account certain margin of enhancements and limitations in existing studies as the subjects of current article. Outcomes of the study are obtained through two most commonly used performance measures, generally known as false alarm rate and power curve. Based on these measures, conclusion of the study shows that proposed structures perform outstandingly as compared to various existing counterparts. In continuation to, design structure for unknown parameters has capability to overcome the issue of existing runs rules, which generally occur when parameters are unknown.

KEYWORDS:

• Control chart
• estimation effect
• false alarm rate
• parameter estimation
• power
• power curve
• runs rules

Acknowledgements

We are thankful to the Editor, Associate Editor and the anonymous Reviewer for providing an opportunity to improve the last version of our paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The author Muhammad Riaz is indebted to King Fahd University of Petroleum and Minerals, Saudi Arabia for providing excellent research facilities under project # IN161037.