Improving the X̄-control chart: A novel scheme based on runs and scans rules

Abstract

To enhance the performance of Shewhart-type control charts for detecting small to moderate shifts, various schemes based on runs and scans rules have been introduced in the literature. This paper introduces a novel scheme based on runs and scans statistics, known as the improved modified runs and scans rules scheme. The proposed runs and scans rules scheme has been applied to the $\bar{X}$-chart and its performance has been evaluated in terms of average run length $\left(\mathrm{ARL}\right)$, standard deviation of run length $\left(\mathrm{SDRL}\right)$ and extra quadratic loss $\left(\mathrm{EQL}\right)$. The results indicate that newly scheme outperforms the existing competitive runs and scans rules schemes. The effectiveness of the improved modified runs and scans rules scheme is demonstrated through a case study of a white millbase process.