Bias and imprecision in variables acceptance sampling Effects and compensation

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Abstract
Variables acceptance sampling plans are designed under the assumption that measurement on the characteristic of interest may be performed without error. To the contrary, variables measurement tasks are often confounded by human inspection error and/or instrument test error. The net result may be characterized in terms of bias and imprecision, where (1) bias is the difference between the true dimension of a unit of product and the average of a long series of repeated measurements on that unit, and (2) imprecision is the dispersion of repeated measurements on the same unit of product. This paper considers the design of variables acceptance sampling plans for a general lot distribution with known and constant variance and either an upper or lower specification limit. Bias, imprecision, and their combined effects on the operating characteristic curve are examined in detail and found to be quite significant. A method is then presented whereby the variables sampling plan may be designed to explicitly compensate for measurement error and provide the desired operating characteristic curve. An example problem is used to illustrate the important results of the paper.

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