Coefficient of variation (CV, RSD)
Definition
The coefficient of variation is a measure of the homogeneity of a batch. It relates the standard deviation s of a series of measurements to the arithmetic mean x and is expressed as a percentage:
CV = (s ÷ x) × 100 %
Internationally, it is often referred to as the relative standard deviation (RSD). Both terms describe the same quantity. A low value indicates that the component under investigation is present in similar concentrations in all samples; in other words, the mixture is homogeneous.
Determination
The coefficient of variation is not measured at the mixer, but on samples. Random samples are taken from the batch at defined points and at defined times, and analysed for the concentration of a reference component. The mean and standard deviation are calculated from the individual values.
The number, location and mass of the samples significantly influence the result: too few samples yield a random result, whilst excessively large sample masses average out inhomogeneities. The sample mass should be based on the intended unit of consumption, such as a tablet, a sachet or a single serving.
Significance and limitations
A low coefficient of variation indicates homogeneity only for the component under investigation, the specific time point and the selected sample mass. It says nothing about whether the mixture remains stable during the subsequent conveying and filling stages; segregation by density, particle size or shape may only occur afterwards. Furthermore, part of the measured variation stems from the sampling and analytical procedures themselves, rather than from the mixing process.
Target values
Target values for the coefficient of variation are application-specific. They are determined by the formulation, the proportion of the main component, the dosage form and the requirements of the customer or the relevant regulations; there is no universally applicable limit value for all applications. It is standard practice to define the target value before the test and to document it together with the sampling plan.
Guideline values for laboratory and pilot-plant trials
When developing and validating new formulations in a vertical mixer, the following threshold values serve as benchmarks:
| Coefficient of variation | Classification |
|---|---|
| less than 3 per cent | very high homogeneity; target range for mixtures containing micro-particles, pigments or active ingredients |
| 3 to 5 per cent | technical homogeneity; the target range typically used in practice for most industrial bulk material mixtures |
These values are intended as a guide for testing and do not replace the target value specified for the particular application.