Sum of Squares Control Charts for Monitoring of Multivariate Multiple Linear Regression Profiles in Phase II

Abstract

In this paper, we propose four control charts for simultaneous monitoring of mean vector and covariance matrix in multivariate multiple linear regression profiles in Phase II. The proposed control charts include sum of squares exponential weighted moving average (SS-EWMA) and sum of squares cumulative sum (SS-CUSUM) for monitoring regression parameters and corresponding covariance matrix and SS-EWMARe and SS-CUSUMRe control charts for monitoring mean vector and covariance matrix of residual. Proposed methods are able to identify the out-of-control parameter responsible for shift. The performance of the proposed control charts is compared with existing method through Monte-Carlo simulations. Moreover, the diagnostic performance of the proposed control charts is evaluated through simulation studies. The results show better performance of the proposed control charts rather than competing control chart. Finally, the applicability of the proposed control charts is illustrated using a real case of calibration application in the automotive industry.

A new Bayesian multivariate exponentially weighted moving average control chart for phase II monitoring of multivariate multiple linear profiles

“…Amiri et al proposed a parameter reduction method for monitoring MML profiles in case the dimension of the vector of regression coefficients is large. Other aspects and applications of MML profiles have been studied by Amiri et al, Ayoubi et al, and Ghashghaei and Amiri . In our study, we focus on the MEWMA control chart in phase II, and we show that its Bayesian variant leads to improved results.…”

“…Other aspects and applications of MML profiles have been studied by Amiri et al, 41 Ayoubi et al, 42 and Ghashghaei and Amiri. 43 In our study, we focus on the MEWMA control chart in phase II, and we show that its Bayesian variant leads to improved results.…”

“…When comparing Equation 42 with Equation 43, it becomes obvious that the Bayesian approach yields different cross-product terms and also assigns different weights to them. In particular, there is a cross-product, where the historical (in-control) estimator "meets" the new estimator.…”

Monitoring simple linear profiles in the presence of generalized autoregressive conditional heteroscedasticity

“…The application of the proposed methods is shown by a real-world case. Ghashghaei and Amiri 30 proposed 4 control charts such as sum of squares (SS) EWMA, SS-CUSUM, SS-EWMARe, and SS-CUSUMRe for simultaneous monitoring of mean vector and covariance matrix in multivariate multiple linear profiles in Phase II.…”

طراحی نمودارهای کنترل مبتنی‌بر باقی‌مانده‌ها برای پایش پروفایل‌های خطی ساده در فرایندهای تولید کوتاه‌مدت

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