Determination of Effectiveness of the ‘Square Root of N Plus One’ Rule in Lot Acceptance Sampling Using an Operating Characteristic Curve

Abstract

Sampling is an inevitable means of testing in quality inspections. However sampling is always associated with sampling risks that inspectors have to control. This paper aims to reveal the reliability and efficacy of the commonly used formula, 'Square root of N plus one', in lot acceptance sampling. An Operating Characteristic Curve is exploited to test the validity of the sampling plan and it offers a further dimension to unveil the unreliability of it. The probability of accepting a defective lot is increased substantially from larger to smaller lot sizes with the deployment of the √N + 1 rule as a sampling plan. Using a sampling plan blindly from recognized sources and pursuing a traditional practice does not ensure that the sampling plan is statistically valid. Regardless of the source of the sampling plan and how it is indexed, it is the actual acceptable quality level (AQL) and lot tolerance percent defective (LTPD) of the sampling plan that describes its protection and determines validity.