Weighted adaptive CUSUM mean chart with variable sample size and sampling interval

Abstract

The classical CUSUM (C) chart is designed by assuming that the size of the shift in the process, in which a quick detection is important, is known a priori. However, this assumption is often violated in practice, as the actual shift size is rarely known even though it may vary within a certain interval. The adaptive C (AC) chart gives better protection against process shifts in a certain interval than the classical C chart. In this paper, we propose a new weighted AC (WAC) chart with the variable sample size and sampling interval (VSSI) feature, which encompasses the fixed sampling rate (FSR), variable sample size (VSS) and variable sampling interval (VSI) based WAC charts. The Monte Carlo simulations are adopted in the run-length computations of the considered charts, where the newly developed (VSS and VSSI based) charts outperform the existing (FSR and VSI) WAC charts when detecting small shifts in the process mean. An illustrative example shows the implementation of the existing and proposed WAC charts.