Optimal Design of Acceptance Sampling Plans by Variables for Nonconforming Proportions When the Standard Deviation Is Unknown

Abstract

This article presents an optimization-based approach for the design of acceptance sampling plans by variables for controlling nonconforming proportions when the standard deviation is unknown. The variables are described by rigorous noncentral Student’s t-distributions. Single and double acceptance sampling (AS) plans are addressed. The optimal design results from minimizing the average sampling number (ASN), subject to conditions holding at producer’s and consumer’s required quality levels. The problem is then solved employing a nonlinear programming solver. The results obtained are in close agreement with previous sampling plans found in the literature, outperforming them regarding the feasibility.

Keywords:

• Acceptance sampling plans by variables
• Nonconforming proportions
• Nonlinear programming
• Unknown standard deviation

Mathematics Subject Classification:

• 62P30
• 90C30
• 90C90