Optimized Design of a Distribution‐Free EWMA Scheme for Individual and Subgroup of Observations and Its Application in Semiconductor Manufacturing

Abstract

This paper addresses the critical challenge of monitoring process location and scale parameters when the underlying distribution is unknown and the magnitude of potential shifts is unspecified. We propose a new Distribution‐Free Double Smoothing Exponentially Weighted Moving Average (DDSE) scheme, which incorporates a two‐dimensional smoothing parameter combination for enhanced flexibility. Traditional joint monitoring statistics assign equal weighting to location and scale shifts, failing to adequately differentiate their distinct impacts on the process. To address this limitation, this paper proposes a novel nonparametric process monitoring scheme based on dual smoothing parameters. We employ three distinct optimization models, Expected Average Run Length (EARL), Expected Quality Loss (EQL), and Relative Mean Index (RMI), to determine the optimal parameter combinations that robustly handle a wide range of unknown shift magnitudes. Extensive Monte Carlo simulations across normal, heavy‐tailed, and skewed distributions demonstrate that the optimally designed DDSE scheme significantly outperforms existing nonparametric alternatives. Finally, we illustrate practical implementation through a flow‐width measurement monitoring case study, confirming industrial applicability.