Title: A Hotelling T² chart for monitoring Gamma regression profile by considering estimation error

Authors: Shiva Isazadeh Khanghah; Ali Salmasnia; Mohammad Reza Maleki; Mehdi Koosha

Addresses: Department of Industrial Engineering, North Tehran Branch, Islamic Azad University, Tehran, Iran ' Department of Industrial Engineering, Faculty of Engineering, University of Qom, Iran ' Industrial Engineering Group, Golpayegan College of Engineering, Isfahan University of Technology, Golpayegan, 87717-67498, Iran ' Faculty of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

Abstract: In some industries, product quality is expressed by a Gamma profile in which a Gamma response variable is functionally associated with one or several explanatory variables. In this paper, the effect of estimation error on false alarm rate and detection capability of the T² Hotelling chart in Phase II monitoring of the Gamma profile is studied. A ten-step framework is developed to extract the average run length (ARL) properties of the T² chart under both in-control (IC) and out-of-control scenarios. In this regard, simulations are implemented to explore how estimation error affects the average of ARL and standard deviation of ARL (SDARL) of the T² chart. The results show that using small samples for estimating Gamma regression parameters during Phase I have two adverse consequences: 1) it significantly increases the false alarm rate, and 2) it reduces the sensitivity of the T² chart to react to out-of-control disturbances.

Keywords: estimation error; Gamma regression profile; T² control chart; average run length properties; phase I reference samples.

DOI: 10.1504/IJQET.2023.132473

International Journal of Quality Engineering and Technology, 2023 Vol.9 No.3, pp.258 - 272

Received: 24 Aug 2022
Accepted: 29 Apr 2023
Published online: 21 Jul 2023 *

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