### STP1400: Assay Variance in a Granular Formulation Can Predict Mixture Homogeneity

Goss, GR

*Oil-Dri Corporation, Chicago, IL*

Hendrix, C

*Consultant in Statistical Methods, South Charleston, West Virginia*

Baldwin, HM

*Oil-Dri Corporation, Chicago, IL*

Pages: 9 Published: Jan 2001

**Abstract**

In granular formulations, the formulator often wishes to spray a small amount of an active ingredient onto a granule. An accurate amount and uniform distribution are the key to product performance in the field. Once product is formulated, the QC lab can provide information on average active ingredient amount. Seldom is there reliable information on active ingredient distribution. Active ingredient distribution can be estimated by observing assay variance. The greater the mixture homogeneity, the less the assay variation and vice versa. Also, the greater the homogeneity of a mixture, the less assay variance is affected by sample size. That is, variation varies inversely with sample size and therefore the number of particles sampled. Or, σ^{2} = k/N where σ^{2} is the variance, k is a constant and N is the number of particles sampled. The value of k will vary inversely with mixture homogeneity. In other words, the value of k will approach zero with a completely homogeneous material or a large enough sample. One can determine mixture homogeneity by determining the variance. Using a single sample size and utilizing the binomial theorem σ^{2} = (A^{2}/pN)(l-p) where A = assay percent active, p = fraction of particles with chemical, and N = number of particles sampled, k from the previous equation is then (A^{2}/p)(l-p). This paper discusses the theory and practicality of this equation.

**Keywords:**

Granule, sampling, variation, pesticide, formulation, probability

**Paper ID:** STP10434S

**Committee/Subcommittee:** E35.22

**DOI:** 10.1520/STP10434S

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