A Robust Control Chart for Monitoring Reliability Systems

Abstract

Control charts are one of the significant statistical control tools widely used to monitor processes. The system’s reliability is affected by failure processes during its lifetime. Monitoring the failure processes is a crucial issue in complex and repairable systems. To design accurate control charts for monitoring a reliability system, it is necessary to estimate the system parameters properly. Since the presence of outliers in sample data can highly affect the parameter estimation using a classic estimator, a robust estimator can estimate the parameters efficiently and close to the actual value in the presence of contamination. In this research, robust monitoring for reliability systems is designed. To estimate the distribution parameters, the robust method based on the M-estimator is used to estimate the time between failure distribution parameters from the Weibull distribution. Using simulation studies, the efficiency of the classic and robust estimators is compared based on the norm and MSE under different contamination scenarios. Then, the robust lower control limit is designed based on the simulated control limit and mathematical formulation methods. The results show that the robust control limits are close to the actual values in the absence or presence of outliers. However, the classic control limits are highly affected by the contamination and their values are far from the actual when there are shifts in the parameter.