Double Sampling Plan Formulation for Quality Assessment

This study addresses the challenge of evaluating service quality under cost constraints by proposing a structured double-sampling framework grounded in acceptance sampling theory. The approach integrates statistical risk control through Type I (?) and Type II (?) error constraints with cost optimization to determine optimal sample sizes (n1, n2) and acceptance thresholds (c1, c2). A two-stage inspection process is developed in which an initial sample enables early decisions, while a second sample is used only when results are inconclusive. The Operating Characteristic function and Average Sample Number are analytically derived to evaluate performance. Simulation-based validation demonstrates reduced inspection cost and improved efficiency compared to single-sampling approaches. The framework provides a practical and statistically reliable method for service quality auditing in sectors such as banking, healthcare, and logistics.