Optimal designing of variables tightened-normal-tightened sampling scheme by minimising the average sample number

Abstract

This paper proposes the optimal designing of variables tightened-normal-tightened sampling scheme for application of measurable characteristics, where the quality characteristic follows normal or lognormal distribution and has upper or lower specification limit. The proposed sampling inspection scheme under variables inspection will be useful when testing is costly and destructive. The advantages of the proposed variables scheme over variables single sampling plan, double sampling plan and attributes sampling scheme are discussed. Tables are also constructed for the selection and application of parameters of known and unknown standard deviation variables sampling scheme for specified two points on the operating characteristic curve. The problem is formulated as a non-linear programming where the objective function to be minimised is the average sample number and the constraints are related to lot acceptance probabilities at acceptable quality level and limiting quality level under the operating characteristic curve.