Effect of Estimation Error on the Monitoring of Multivariate Multiple Linear Profiles in Phase II

Functional relationships between a response variable and one or more explanatory variables for monitoring product or process quality are quite common in practice. This relationship is generally known as a profile, with parameters that are often unknown and need to be estimated before online monitoring can begin. Phase II of the analysis starts once a statistically in-control condition has been established and the parameters of the underlying distribution have been estimated. It is evident that the Phase II analysis of control charts is affected by errors in these estimated parameters. This paper explores the impact of estimation errors on the Phase II analysis of multivariate multiple linear profiles. In this regard, we consider MEWMA and MEWMA method in low-dimensional space approaches for monitoring these profiles. We compare these methods in terms of their estimation errors. The comparison is carried out under the assumption of estimated parameters using the AARL, SDARL, and CVARL metrics. The simulation results show that generally the MEWMA in low-dimensional space method performs better in terms of the CVARL criterion and needs fewer Phase I samples.

کلیدواژه ها:

Multivariate multiple linear regression profiles ، Estimation error ، Control chart