A novel robust control chart for monitoring multiple linear profiles in phase II

Abstract

A profile is a relationship between the response variable(s) and the independent variable(s), which describes the quality of a process or product. The profile can be monitored by a process control chart, which is an important tool in the statistical process control. Using the robust estimators in monitoring profiles in the presence of contamination is so effective, and it improves the efficiency of a control chart in detecting any sustained shift in phase II. In this research, a novel robust control chart is proposed for monitoring multiple linear profiles using two robust estimate methods. In the proposed robust control chart, the parameters of a multiple linear profile are estimated using the M-estimator and the Fast-τ-estimator. Also, the efficiency of the proposed robust control chart is evaluated by means of ARL criterion and compared to the classic control chart in phase II. The results of simulation studies show that the proposed robust control chart performs as well as the classic control chart in the absence of contamination, while in the presence of contamination, it can detect the shifts quicker than the classical one. Moreover, the proposed robust control chart using Fast-τ-estimator and M-estimator performs better in low and high contamination, respectively.

Keywords:

• Average run length (ARL)
• Multiple linear profile
• Outliers
• Robust control chart
• Robust estimators
• Statistical process control