The mathematical model for estimating the probability of risk of incompetent specialist graduation

Abstract

The article presents the results of research for the mathematical model for estimating the probability of risk of incompetent specialist graduation. The mechanisms and tools to determine the probability of risk of incompetent specialist graduation have been developed in the course of the research. The goal tree method has been used as a mechanism to determine the relationship between the structural components of the educational process and the educational program. Using this method, the structuring of 9 criteria by which the educational program quality is evaluated has been carried out. That is, its strengths and weaknesses have been identified. In turn, as a tool for estimating the probability of an educational process (educational program) risks and the graduation of an incompetent specialist, it has been proposed to use a regression mathematical model. To build a mathematical model, an active experiment, a qualimetric approach, a method of regression analysis, and 16 conditional educational programs that met the "Standards and Guidelines for Quality Assurance in the European Higher Education Area" (ESG) have been used. The construction of the model has been carried out according to a specially designed scheme, which included 5 stages. In the first stage, a group of experts was formed and their consistency was determined with the help of the "HEI Experts" software. In the second stage, six groups of indicators were identified, which further estimated the educational process (educational program) quality. For this purpose, the experts used the method of pairwise comparison to select 9 unit indicators, which further estimated the levels of compliance of 16 conditional educational programs. The estimation was conducted according to standardized quality indicators that are inherent in the real educational process (educational program). In the third stage, a robust plan of the experiment was constructed using the method of pseudo-random LP-τ numbers uniformly distributed in multidimensional space. According to the plan, a working matrix of the experiment was formed. Then, the group of experts formed in the first stage carried out the percentage estimation of the probability of risk of incompetent specialist graduation. In the fourth stage, a mathematical model was built using the PRIAM (planning, regression, and model analysis) software. This model allows us to assess nine factors that affect the probability of risk of incompetent specialist graduation. In the fifth stage, the statistical characteristics of the model were tested. According to the test results, it was proved that the model is informative, adequate, and stable, both in terms of structure and calculations. At the same stage, the marginal surfaces were constructed and the forces of influence of regressors (indicators) on the probability of risk of competent/incompetent specialist graduation were determined. According to the results of research, it has been proved that such indicators as compliance of the applicants (bachelors) level with the second Master's level and the level of considering labor market employers (stakeholders) requirements have the strongest impact on the competence of the future specialists. The proposed model allows us to estimate the factors influencing the efficiency (effectiveness) of the educational process and to determine the probability of the risk of competent/incompetent specialist graduation.