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Abstract

The implementation of attribute-based sampling inspection serves as a quality control technique used across numerous industries to evaluate items or workflow processes. When the data exhibits a substantial number of zero counts, the zero-inflated Poisson (ZIP) distribution serves as an effective model for accommodating this zero-inflation. Double sampling plan (DSP) is a quality check method where the decision to approve or decline a batch comes after examining two samples, providing more conclusive information compared to a single sample plan (SSP). In practice, effective decision-making regarding submitted lots considers both within-lot and between-lot variations, which can be addressed through the use of Bayesian methodology. The Bayesian approach facilitates more informed decision-making concerning the acceptance or rejection of a batch by incorporating prior knowledge about nonconformities. This article presents the designing Bayesian DSPs when the count of nonconformities per products follows a ZIP distribution. Employing a Gamma prior to the parameter in the Poisson component, the operating characteristic (OC) and average sample number (ASN) functions are derived with reference to the predictive distribution. Examples are provided to determine Gamma - ZIP (GZIP) DSPs.

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