An optimization-based framework for designing acceptance sampling plans by variables for non-conforming proportions

• Published in: The International journal of quality & reliability management 2010-01, Vol.27 (7), p.794-814
• Main Authors: Duarte, Belmiro P.M, Saraiva, Pedro M
• Format: Article
• Language: English
• Subjects: Acceptance; Acceptance sampling; Algorithms; Approximation; Binomial distribution; Design; Linear programming; Mathematical analysis; Mathematical models; Mathematical programming; Mixed integer; Nonlinearity; Normal distribution; Optimization; Optimization techniques; Probability; Product quality; Production management; Quality control; Sample size; Sampling; Standard deviation; Studies
• ISSN: 0265-671X; 1758-6682
• DOI: 10.1108/02656711011062390

Purpose - This paper seeks to present an optimization-based approach to design acceptance sampling plans by variables for controlling non-conforming proportions in lots of items. Simple and double sampling plans with s known and unknown are addressed. Normal approximation distributions proposed by Wallis are employed to handle plans with s unknown. The approach stands on the minimization of the average sampling number (ASN) taking into account the constraints arising from the two point conditions on the operating characteristic (OC) curve. The resulting optimization problems fall under the class of mixed integer non-linear programming (MINLP), and are solved employing GAMS. The results obtained strongly agree with classical acceptance sampling plans found in the literature, although outperforming them in some cases, and providing a general approach to address other cases.Design methodology approach - The approach takes the form of formulation of the design of acceptance sampling plans by variables for non-conforming proportions as optimization problems minimizing the ASN with the constraints being the acceptance probability at the controlled points of the OC curve, and subsequent solution of the mathematical programming problems arising with mathematical programming algorithms.Findings - The results are in strong agreement with acceptance sampling plans available in the literature. The approach presented here outperforms the classical plans in some cases and its generality allows one to design other plans without the requirement of additional relations between the parameters and intensive enumerative algorithms.Originality value - The paper presents an optimization-based approach to design robust acceptance sampling plans by variables for non-conforming proportions that allows a general treatment and disregards the need for computational intensive enumerative-based procedures.