Statistical monitoring of multivariate multiple linear regression profiles in phase I with calibration application

Abstract

In some statistical process control applications, there are some correlated quality characteristics which can be modeled as linear functions of some explanatory variables. We refer to this structure as multivariate multiple linear regression profiles. When the correlation structure between quality characteristics is ignored and profiles are monitored separately then misleading results could be expected. Hence, developing methods to account for this multivariate structure is required. In this paper, we specifically focus on phase I monitoring of multivariate multiple linear regression profiles and develop four methods for this purpose. The performance of the developed methods is compared through simulation studies in terms of probability of a signal. In addition, a diagnostic scheme to find the out-of-control samples is developed. Finally, the application of the proposed methods is illustrated using a calibration application at the National Aeronautics and Space Administration (NASA) Langley Research Center.

Phase II monitoring of multivariate multiple linear regression profiles

“…This case, which is referred to as multivariate multiple linear regression profiles, consists of several correlated response variables where each response is modeled by a multiple linear regression. Noorossana et al 31 proposed four methods including likelihood ratio, Wilk's lambda,T 2 , and principal components analysis to monitor multivariate multiple linear regression profiles in Phase I.…”

Profile Monitoring for Compositional Data

“…If a process is modeled using the multivariate normal regression, the response variables can take any real value, (Noorossana, Eyvazian, Amiri & Mahmoud 2010). However, this assumption is not met here, because the response variables for compositional data are always positive and range only from 0 to 100, or any other constant.…”

“…Several control chart approaches for monitoring simple linear profiles have been developed by Kang & Albin (2000), Kim, Mahmoud & Woodall (2003), Zou, Zhang & Wang (2006), Zou, Zhou, Wang & Tsung (2007), Mahmoud, Parker, Woodall & Hawkins (2007), Soleimani, Narvand & Raissi (2013), Zhang, He, Zhang & Woodall (2013), Yeh & Zerehsaz (2013) and Amiri, Zou & Doroudyan (2014). Proposals for monitoring multivariate linear profiles (simple and/or multiple) have been developed by Mahmoud (2008), Noorossana, Eyvazian & Vaghefi (2010), Noorossana, Eyvazian, Amiri & Mahmoud (2010), Eyvazian, Noorossana, Saghaei & Amiri (2011) and Zou, Ning & Tsung (2012).…”

Maximum Multivariate Exponentially Weighted Moving Average and Maximum Multivariate Cumulative Sum Control Charts for Simultaneous Monitoring of Mean and Variability of Multivariate Multiple Linear Regression Profiles

“…They also used the term Average Run Length (ARL) to evaluate the proposed control charts. Noorossana et al [19] developed four control charts in Phase I for monitoring of multivariate multiple linear regression pro les. They compared the performance of the proposed control charts through simulation studies in terms of probability of a signal.…”