Integrating capability index and generalized rule-switching mechanism for enhanced quick-switch sampling systems

Variables Quick-Switch Sampling Systems (VQSSs) that involve both normal and tightened inspections for lot dispositions have attracted significant attention and discussion. However, existing VQSS models exhibit limitations, particularly in their rule-switching mechanism. Practitioners may encounter situations where multiple rounds of tightened inspection are necessary to ensure submission quality when suspicions of process degradation arise. Current VQSS models do not effectively address this need. To overcome this limitation, we present VQSSG by integrating a VQSS with a generalized rule-switching mechanism and the widely used capability index Cpk. VQSSG offers practitioners the flexibility to specify the number of successive lot acceptances under tightened inspection before transitioning to normal inspection. Our research includes the derivation of operating characteristics and average sample number functions for VQSSG, based on the Cpk index. Through in-depth investigations, we construct nonlinear optimisation models to determine the optimal system design and identify distinct types and settings for VQSSG, highlighting its strengths and weaknesses. Additionally, we provide managerial insights and recommendations for the effective implementation and application of VQSSG. To validate the practicality of this system, an industrial case study is presented. This paper significantly enhances the efficiency and adaptability of sampling systems by introducing VQSSG. The findings and managerial suggestions contribute to a deeper understanding of potential real-world applications, thereby enhancing quality control and decision-making processes.