Design of the sum-of-conforming-run-length control charts

The sum of conforming run lengths (SCRL) control chart is a powerful charting technique for detecting the p (fraction nonconforming) shift in a process. In this article, the general formulae for designing the control limits and evaluating the out-of-control average time to signal of the SCRL chart are presented. The formulae are developed based on the random-shift model whereby the p shift may occur at any point with an SCRL sample. The proposed formulation can facilitate the design and assessment of the SCRL chart, thus promoting its application in practice.