A Hotelling T2 chart for monitoring Gamma regression profile by considering estimation error Online publication date: Fri, 21-Jul-2023
by Shiva Isazadeh Khanghah; Ali Salmasnia; Mohammad Reza Maleki; Mehdi Koosha
International Journal of Quality Engineering and Technology (IJQET), Vol. 9, No. 3, 2023
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.
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