Сборник статей VI международной научно-практической конференции, Состоявшейся 20 ноября 2021 г в г. Пенза
ИСПОЛЬЗОВАНИЕ МНОГОМЕРНОЙ СТАТИСТИЧЕСКОЙ МЕТОДОЛОГИИ В ОЦЕНКЕ
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- ТЕОРИЯ И ПРАКТИКА СОВРЕМЕННОЙ НАУКИ
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ИСПОЛЬЗОВАНИЕ МНОГОМЕРНОЙ СТАТИСТИЧЕСКОЙ МЕТОДОЛОГИИ В ОЦЕНКЕ
КОНКУРЕНТОСПОСОБНОСТИ ПРЕДПРИЯТИЙ Сакиева Озода Батировна Аннотация: В статье приведены теоретические данные методов многомерного статистического анали- за для применения методов таксономического и иерархического анализа при оценке конкурентоспо- собности продукта предприятия.
арифметические вычисления, отклонение. ТЕОРИЯ И ПРАКТИКА СОВРЕМЕННОЙ НАУКИ
𝑆 𝑘 = [
1 𝜔 ∑ (𝑥 𝑖𝑘 − 𝑥 𝑘 ̅̅̅)
2 𝜔 𝑖=1 ] 1 2 (2) is calculated based on the formula. We use the following formulas for standardization: 𝑍 𝑖𝑘
𝑥 𝑖𝑘 −𝑥 𝑘 ̅̅̅̅
𝑠 𝑘 (3) Where k = 1,2, …, n;𝑥 𝑖𝑘 – i – k –indicator value per unit; 𝑥 𝑘 ̅̅̅is the arithmetic mean of k; 𝑆 𝑘 is the stand- ard deviation of the k indicator; 𝑍 𝑖𝑘 - i - standardized value of k for the unit: a matrix of observations is made on the calculated values of the standardized indicators. The matrix indicators are differentiated, for example, the matrix values determine the positive and negative factors that affect the level of product quality develop- ment.The level of quality of each product is a benchmark for development ℎ 0 = с 0 ̅ + 2𝐹 0 (4) is calculated based on the formula, where с 0
1 𝑤 ∑ 𝑐 𝑖0 ; 𝑤 𝑖=1
(5)𝐹 0 = [ 1 𝑤 ∑ (𝑐 𝑖0 − с 0 ̅ )
2 𝑤 𝑖=1 ] 1 2 (6) Now the level of development of each truck is an indicator of 𝑑 𝑖
𝑖 = 𝑐 𝑖0 ℎ 0 (7)is calculated separately based on the formula. According to the theory of taxonomic analysis, the closer the 𝑑 𝑖 indicator is to 0, the higher the level of product quality development. In addition to this method, the hierarchical analysis method is also one of the methods of multidimen- sional statistical analysis, which is a mathematical method of a systematic approach to solving decision- making problems. This method was developed by the American scientist Thomas Saati in 1970 and is widely used in practice. A.S. Vinokurov, R.I.Bajenov, G.G. Azgaldova, O.V. Daneev, G.L. Brodetskiy, P.A. Terentev, Tsibizova, A.A. Karpunin, O. in Uzbekistan. S. Kahkhorov used this method effectively in assessing the effec- tiveness of the management of educational institutions. According to this method, n alternative solutions are given to achieve the overall goal of the existing system activity, each alternative is evaluated by experts on the basis of selected m criteria. Let it be required to choose the most optimal of them. The solution of the problem consists of the following steps: 1. The first problem is formed in the form of a hierarchical structure: goal-alternative-criterion. 2. The selected m criteria are compared in pairs. If we define the percentage of the i-criterion as w i , then
a 𝑎 𝑖𝑗 = 𝑤 𝑖 𝑤 𝑗 . In this case, it is not the magnitude of the difference in the values of the criteria, but their relation- ship - that is, 𝑎 𝑖𝑗 = 𝑤 𝑖 𝑤 𝑗 . If the element i is more important than the element j during the filling of the matrix, the integer is entered in cell (i, j), and the fractional number is entered in cell (j, i). If of equal importance, the num- ber 1 is entered, so that the main diagonal elements consist of 1s. This means that the elements of the pairing matrix are in the form of a positively defined inverse matrix with a color of 1. When filling in the table, they are compared in pairs using the appropriate square matrix (nxn) on a 9- point scale, taking into account their previous higher-level characteristics. In this case, each element of the matrix [а ij ] is built on the importance of the hierarchies I and j; in other words, the results of a separate compar- ison are given by the appropriate matrices, taking into account then decision of the decision-maker or expert (group of experts). The distribution of points is as follows: 1 - equal importance, 3 - a slight advantage, 5 - a sufficient advantage, 7 - a strong advantage and 9 - a very strong advantage, in intermediate cases 2,4,6,8 points are given. b Based on the values found in the third step, the significance coefficients of the specific vector compo- nent of each comparison matrix are found for the level comparison elements of the corresponding hierarchy. The results of this work are formed in the form of special tables, and its algorithm is as follows: 1. In the table, additional column elements are first found according to the corresponding comparison matrix. In this case, the elements of the series are multiplied. 2. For the comparison matrix, the eigenvector with component Sx is determined on the basis of j-level root derivation from additional column elements. 3. Then the eigenvector is normalized; in other words, the ratio of eigenvector elements to the sum of eigenvector elements is determined.
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