Empirical Comparisons of &Xmacr; Charts when Control Limits are Estimated

A control chart is a very common tool used to monitor the quality of business processes. An estimator of the process variability is generally considered to obtain the control limits of a &Xmacr; chart when parameters of the process are unknown. Assuming Monte Carlo simulations, this paper first compares the efficiency of the various estimators of the process variability. Two empirical measures used to analyze the performance of control charts are defined. Results derived from various empirical studies reveal the existence of a linear relationship between the performance of the various estimators of the process variability and the performance of &Xmacr; charts. The various Monte Carlo simulations are conducted under the assumption that the process is in both situations of in‐control and out‐of‐control.