Robust Process Capability Indices for Multivariate Linear Profiles

Abstract

The quality of a product or process is an important issue for both customers and producers. The quality could be defined as a linear relationship between the response variable (s) and explanatory variable (s), which is called a linear profile. Another essential concept in quality control is the adaptation of quality specifications with customers' standards. The proper tool to measure customers' specifications is process capability indices (PCIs). To find the PCIs for profiles, the profile parameters should be estimated. These parameters can be estimated using classic estimators. However, in the presence of outliers, the classic estimators do not estimate the parameters accurately. Therefore, the performance of the classic indices using classic estimators is appropriate only in the absence of contamination. In this research, robust estimate methods such as M-estimator and LR-weighted MCD estimators are used to propose robust PCIs for multivariate linear profiles. The proposed robust indices include C <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pm</inf> and MC <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">pc</inf> for a multivariate linear model. The performance of the proposed robust PCIs is compared with the classic PCIs in the absence and presence of contamination. The result of simulation studies shows that robust PCIs perform better than classic PCIs in the presence of outliers. In the absence of contamination, the robust PCIs perform as accurately as classic PCIs. The proposed PCIs using LR-weighted MCD outperform the M-estimator method in all considered contamination scenarios.