Use of Harrington’s desirability function in wheat grain quality assessment

Abstract

The publication is devoted to the development of a method for assessing the quality of wheat grain based on Harrington’s desirability function, which reflects the nonlinearity of the relationship between the quantitative values of quality indicators and the psychological perception of a person. As an empirical base, we used the results of studies on the protein content, gluten content and sedimentation index – Zeleny test of more than 40 varieties of winter wheat, zoned in the Oryol region, the main analysis tool was the factor analysis by the method of principal components. It is substantiated that the set of these wheat grain quality indicators can be described with one slight distortion by one main factor, along with particular desirability functions used to construct a generalized quality indicator with linguistic levels “very good”, “good”, “satisfactory”, “bad” and “very bad”. The calculation of the values of the main factor of wheat varieties, which are absent in the initial data array, is proposed using an approximate formula that takes into account the indicator that is most closely correlated with it - the protein content. The proposed methodology was tested on the example of assessing the influence of sowing dates on the productivity of winter wheat variety Moscow 39. Based on the results of the studies, it is recommended to use the Harrington’s transformation to evaluate particular indicators of the quality of wheat grain. It is also promising to use the method of principal components for the formation of a generalized function of desirability, when the weights of particular indicators are taken into account “automatically” by using the main component as a normalized variable, which comprehensively reflects the quality of wheat grain.

Evaluation of the influence of sowing time on yield and quality of the wheat grain using Multivariate dispersion analysis

“…The interpretation of the variance analysis model parameters is explained by the linear yield model (Table 7). 7 shows Least Squares (LS) estimates of model parameters (1). In it, the constant is 000=47,3 dt/ha, and the effect of option 5 is taken as zero, that is, the yield of wheat grain with the sowing date shift by 40 days is 47.3 dt/ha.…”

“…In addition, the quality indicators are positively and strongly correlated with each other, which is of clear interest to combine them into a kind of generalized quality indicator. It is recommended to use the Harrington desirability function normalized to the interval (0; 1) [8] as such an indicator as it was implemented in our previous work [1]. In this work, Harrington's generalized desirability function was determined from the array of 46 varieties, and then used to assess the quality of Moskovskaya 39 wheat grain depending on the sowing date; at the same time, the assessment "well" and "satisfactorily" corresponded to the sowing date shift by 10-20 days.…”

“…Winter wheat sowing at a later date increases the length of the field preparation period, which leads to the increase in yields and affects positively the quality improvement. So, in the work [1] on the example of the wheat variety Moskovskaya 39, it was shown that sowing at a later date ensured an increase in grain-unit, protein and gluten accumulation in the grain by 8-24 gram per liter, 0.7-1.3%, an increase in yield by 0.14-0.33 t/ha respectively, in comparison with the recommended period.…”

Selecting the best planter option based on Harrington function

“…The value of the weighting coefficient ki, was taken depending on the importance of the particular estimated indicator ji (Table 2). The Harrington desirability function has long been widely used in various scientific fields [20][21][22]. In relation to the task set, it has been modernized in graphical form [23][24].…”