Designing economic-statistical Hotelling’s T 2 control charts for monitoring linear profiles under uncertainty of parameters

Abstract

This paper proposes a robust economic-statistical design for Hotelling’s T2 control chart to monitor linear profiles, accounting for uncertain parameters. Unlike previous studies assuming fixed inputs, this work applies an uncertainty interval approach to address parameter uncertainty when investigating the T2 chart design. In this way the challenge of parameter uncertainty's adverse impact on the effectiveness of quality control models in practice is addressed. The key contribution of this study is formulating a T2 control chart that maintains accuracy despite uncertainty. Results demonstrate the value of increased costs to mitigate uncertainty risks. The proposed approach also facilitates selecting appropriate protection levels against uncertainty. The paper examines practical challenges and applications of implementing the T2 chart under real-world conditions affected by uncertainty. Overall, the proposed robust T2 control chart design incorporates parameter ranges for monitoring linear profiles, contrasting with previous models assuming fixed parameters.

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