Pareto-Front Optimization of Variance-Added Expected Loss with Interrelated Qualities

In industries, particularly in quality optimization, the trade-off between model bias and variance is inevitable, reflecting the tension between accuracy and uncertainty. Traditional methods often address these aspects separately, potentially leading to suboptimal decisions. This study proposes a Pareto-front optimization framework for a variance-added expected loss function within the context of interrelated quality characteristics. By integrating multivariate quadratic loss with a variance term, our approach simultaneously captures deviation from targets (bias) and system uncertainty (variance). Unlike sequential approaches that first minimize bias and then variance-often increasing total risk-our weighted formulation flexibly adjusts for their trade-offs. This enables a more balanced and efficient optimization process that identifies solutions with lower overall risk. Through Pareto-front analysis, we reveal trade-offs between expected loss and variance, allowing users to select optimal quality designs based on their preferred bias-variance balance. Representative examples and a case study adopted from the literature validate the effectiveness and practical applicability of the proposed method.