A Self-starting Control Chart for Simultaneous Monitoring of Mean and Variance of Simple Linear Profiles

Abstract

In many processes in real practice at the start-up stages the process parameters are not known a priori and there are no initial samples or data for executing Phase I monitoring and estimating the process parameters. In addition, the practitioners are interested in using one control chart instead of two or more for monitoring location and variability of processes. In this paper, we consider a simple linear profile in which the relationship between a response variable and one explanatory characterizes the quality of a process. We proposed a self-starting Max-CUSUM control chart based on recursive residuals to monitor mean vector (including intercept and slope) and variability (variance of error term) of a simple linear profile simultaneously from the start-up stages of the process. We developed Max-CUSUM control chart to monitor simple linear profile in Phase II. Then, we compared our proposed control charts with the best one in the literature through simulation studies. The simulation results showed that our proposed control charts have better performance compared to competitive control charts under moderate and large shifts in terms of out-of-control (OC) ARLs. Finally, the application of the proposed self-starting control chart is illustrated through a real case in the leather industry.