An EWMA sign chart for monitoring processes with fixed and variable sample sizes

Abstract

This study addresses limitations in the nonparametric EWMA sign chart with fixed control limits (FCLs), particularly when facing time-varying sample sizes. The FCLs-based EWMA sign chart has a variable conditional false alarm rate (CFAR), especially at the startup of a process or after recovering from an out-of-control signal. To overcome these limitations, we propose a nonparametric EWMA sign chart based on dynamic probability control limits. This chart is capable of monitoring the process target with fixed, as well as time-varying sample sizes. Monte Carlo simulations are used to estimate the CFARs, zero-state (ZS) and steady-state (SS) average run-length profiles of the EWMA sign charts. It turns out that the proposed chart outperforms the existing chart, particularly in detecting shifts during the process startup, while maintaining the desired CFAR levels in both ZS and SS scenarios. A real data example is given to demonstrate the implementation of the EWMA sign charts.