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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 54 Issue: 4

Efficient techniques for designing and evaluating multivariate Hotelling control chart with generalized sensitizing rules

Rashid Mehmood(University of Hafr Al Batin, Saudi Arabia)0000-0002-0993-4665
Muhammad Naveed Khan(Univeristy of Hafr Al Batin)0000-0001-8961-1358
Iftikhar Ali(University of Hafr Al Batin)0000-0002-0371-2973
Tajammal Imran(University of Hafr Al Batin)0000-0002-8119-2432
Babar Zaman(GIKI of Engineering Sciences and Technology)0000-0003-1259-1429
Kassimu Mpungu(Mountain of the Moon University)0000-0002-8669-6621
Fawwad Qureshi(Abu Dhabi Univeristy)0009-0006-6961-335X
Maysaa Elmahi Abdelwahab(Princess Nourah bint Abdulrahman University)0009-0000-7059-405X
Pages
—
Publication Date
2025-08-29
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The results indicate that the proposed control chart has consistent behavior when a process is in control.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, efficient techniques are utilized to design the multivariate Hotelling control chart with sensitizing rules for detecting small-to-moderate variations.
📊
Key Findings & Data:For evaluation, performance measures are considered based on the average, the median, and the percentile run length.
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Conclusion & Impact:The results indicate that the proposed control chart has consistent behavior when a process is in control.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Average run length · Hotelling · median run length

Abstract

In this study, efficient techniques are utilized to design the multivariate Hotelling control chart with sensitizing rules for detecting small-to-moderate variations. The control limit of the proposed chart is derived relative to probability of a single point and number of process characteristics. To calculate probability of a single point for sustained in-control average run length, a generalized single polynomial equation is derived. For evaluation, performance measures are considered based on the average, the median, and the percentile run length. These measures are calculated using Monte Carlo simulation and numerical integration. The results indicate that the proposed control chart has consistent behavior when a process is in control. The in-control average run length is obtained equal to prefixed level which remains valid for all choices of sensitizing rules. This implies that the proposed control chart can resolve the issue of existing control chart in terms of sustained behavior. The effectiveness of sensitizing rules is dependent on process characteristics and variations of mean vector. A comparative analysis of different choices of sensitizing rules is conducted to locate optimal choices of process characteristics. Real-life example, dowel-pin manufacturing, shows that proposed control chart with sensitizing rules is efficient for diagnosing small variations.

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Cite This Article

Mehmood, R., Khan, M. N., Ali, I., Imran, T., Zaman, B., Mpungu, K., Qureshi, F., Abdelwahab, M. E. (2025). Efficient techniques for designing and evaluating multivariate Hotelling control chart with generalized sensitizing rules. Hacettepe Journal of Mathematics and Statistics, Volume: 54 Issue: 4. https://doi.org/10.15672/hujms.1541132

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