The Lognormal Distribution for Modeling Quality Data When the Mean is near Zero

Abstract

The standard approach for dealing with lognormal data is to transform it to normal data by taking the natural log of each observation. This presents a problem for acceptance sampling applications: the producers and consumers need to express their quality requirements in units that have meaning to the product of interest. Here, we bridge the gap between the units of the product of interest and the units of the log-transformed data with formulas to determine required sample size and to construct Operating Characteristic curves for sampling plans. The work was motivated by a project that was set up to design acceptance sampling plans for the minute amounts of aluminum impurity in recycled plastic material. The lognormal distribution provided a useful model for this data having a mean near zero.

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