For the determination of kefir grain mass, the gravimetric method was used. Therefore, kefir grains were separated first from the fermentation medium with plastic household sieve. Then the grains were washed with cold water and dried on filter paper to remove of bulk of adhered water. Finally, kefir grain mass was determined by weighting on Mettler-Toledo analytical balance (PG5002-S).

1.3 Taguchi’s experiment design methodology

Dr. Genichi Taguchi has defined the optimization criterion quality as a consistency in achieving the desired or targeted value and minimization of the deviation (Ranjit, 1990). This goal is connected with the performance of a series of experiments with different bioprocess parameters at different levels. The bioprocess parameter is a factor affecting the optimization criterion quality, and its value is called the ‘level’. The number of experiments and their sequence are determined by standard OA. When planning the experiments using four bioprocess parameters at four levels, we use the OA L16. Such a plan envisages the performance of 16 experiments, which is significantly less when compared to the full factorial DoE with 44 = 128 experiments.

Due to performing only a part of the envisaged experiments using the traditional full factorial DoE methodology, it is necessary to include an analysis of the results confidence. The standard statistical technique is used for this purpose, the so-called ‘analysis of variance’ (ANOVA), which recognizes the relative impact of the bioprocess parameters for the optimization criterion (in our case daily kefir grain increase mass) value.

The mathematical algorithm of the ANOVA statistical technique is based on calculation of the variance, which is an indicator of the optimization criterion quality. The ratio between the variance of the bioprocess parameter and the error variance shows whether the parameter affect on the product’s quality. The equations required for calculating the relative impact of various significant bioprocess parameters affecting the optimization criterion are presented bellow. The meanings of symbols are described in the sub-chapter "Nomenclature".

We compare variance ratio of bioprocess parameter j, Fj, to the standardized value at defined level of significance, Fm, n, which is obtained from the standard F tables (Ranjit, 1990), whereby m stands for the degree of freedom of bioprocess parameter j and n means the degree of freedom of error variance, and thus determine the bioprocess parameter impact accordingly. In the case where the variance ratio of bioprocess parameter j falls below Fm, n, the bioprocess parameter has no impact on the optimization criterion, therefore, it is pooled and ignored in the calculations. Consequently, the variance error changes, as the sum of squares and degree of freedom of the pooled bioprocess parameter are added to the error sum of squares and degree of freedom of error variance, respectively. By using the adjusted variance error, we determine new variance ratio of bioprocess parameter j and compare them again by the Fm, n. The process of pooling is sequential, which means that the parameter having the smallest impact on the optimization criterion should be pooled first, then we re­calculate the variance ratio of bioprocess parameter j and continue pooling until each bioprocess parameter meets the condition Fj > Fm, n. If the pooling process begins to perform, Taguchi recommends pooling bioprocess parameters until the degree of freedom of error variance is approximately half the total degree of freedom irrespective of significant test criterion validity Fj > Fm, n for all remaining bioprocess parameters (Taguchi, 1987). When the pooling procedure is completed, the relative impact of bioprocess parameter j and error on optimization criterion can be calculated using Eqs. (10) and (11).