Two Economically Optimized Nonparametric Schemes for Monitoring Process Location and Scale

Several distribution‐free control charts have been developed for joint monitoring of process location and scale under unknown process distributions. Their statistical performance has been well studied, but the economic‐statistical design of such charts has received limited attention. This study develops an economic‐statistical design framework for nonparametric joint location‐scale monitoring. Two Lepage‐type schemes are constructed by combining the van der Waerden statistic with either the Ansari‐Bradley or the Mood statistic. Sample size, sampling interval, and control limits are optimized together to minimize the expected cost per unit time, subject to a false‐alarm constraint. The framework estimates the false‐alarm and Type II error probabilities within the optimization using Monte Carlo simulation and bootstrap, which makes economic design feasible without closed‐form expressions. Numerical experiments cover several distributions and process scenarios, and the proposed schemes perform well in both statistical and economic terms. A case study on coating thickness data from lithium‐ion battery electrode manufacturing shows how the framework can be applied in practice.