Phase II monitoring of multivariate simple linear profiles with estimated parameters

In some applications of statistical process monitoring, a quality characteristic can be characterized by linear regressionrelationships between several response variables and one explanatory variable, which is referred to as a “multivariate simplelinear profile.” It is usually assumed that the process parameters are known in Phase II. However, in most applications,this assumption is violated; the parameters are unknown and should be estimated based on historical data sets in Phase I.This study aims to compare the effect of parameter estimation on the performance of three Phase II approaches for monitoringmultivariate simple linear profiles, designated as MEWMA, MEWMA_3 and MEWMA∕2 . Three metrics are usedto accomplish this objective AARL, SDARL and CVARL. The superior method may be different in terms of the AARL andSDARL metrics. Using the CVARL metric helps practitioners make reliable decisions. The comparisons are carried outunder both in-control and out-of-control conditions for all competing approaches. The corrected limits are also obtained bya Monte Carlo simulation in order to decrease the required number of Phase I samples for parameter estimation. The resultsreveal that parameter estimation strongly affects the in-control and out-of-control performance of monitoring approaches,and a large number of Phase I samples are needed to achieve a parameter estimation that is close to the known parameters.The simulation results show that the MEWMA and MEWMA∕2 methods perform better than the MEWMA_3 method interms of the CVARL metric. However, the superior approach is different in terms of AARL and SDARL.