An efficient approach of designing distribution-free exponentially weighted moving average schemes with dynamic fast initial response for joint monitoring of location and scale

Abstract

An EWMA scheme with the fast initial response (FIR) feature usually detects an initial out-of-control (OOC) situation much quicker compared to a standard EWMA scheme. Researches on EWMA schemes with the FIR feature primarily focussed on their OOC performance, ignoring the fact that the FIR feature may increase the number of false alarms at the early stage of monitoring. In this paper, we introduce the concept of an EWMA scheme with a dynamic FIR feature that restricts initial false alarms and also improves OOC performance. We discuss a data-dependent approach based on Kernel density estimation for the design parameters. We use the proposed concept in designing distribution-free FIR-based EWMA schemes for joint monitoring of location and scale. Simulation results demonstrate that our proposed procedure generally performs well under various continuous distributions. We illustrate the application of our proposed schemes using two sets of data arriving out of the manufacturing sector.