The problem of assessing the quality of the open-source software, including web applications developed using the PHP frameworks, is important because nowadays the popularity of open-source software is growing, and web application development is performed using frameworks. The object of the study is the process of assessing the quality of open-source web applications developed using PHP frameworks, using software metrics RFC (Response for Class), CBO (Coupling Between Objects), and WMC (Weighted Methods per Class). The subject of the study is the mathematical models to evaluate the quality of the open-source web applications developed using the PHP frameworks, using the software metrics RFC, CBO, and WMC. The objective of the paper is to improve a mathematical model for assessing the quality of open-source web applications developed using PHP frameworks, which will allow us to increase the confidence to determine the quality of these applications according to the software metrics RFC, CBO, and WMC. Methodology. To construct the specified mathematical model, we use methods of nonlinear regression analysis based on multivariate normalizing transformations. As a multivariate normalizing transformation, we apply the three-variate Box-Cox transformation, the parameter estimates of which are computed using the maximum likelihood method. The scientific novelty of this study lies in the improvement of the mathematical model in the form of confidence and prediction intervals of nonlinear regressions for RFC, CBO, and WMC metrics at the application level for software quality assessment based on the three-variate Box-Cox transformation, which, unlike existing models, allows for appropriate assessment for open-source web applications developed using PHP frameworks. The results obtained have scientific and practical significance for assessing the quality of open-source web applications developed using such well-known PHP frameworks as CakePHP, CodeIgniter, Laravel, Symfony, and Yii, according to data from their RFC, CBO, and WMC software metrics and can be used for further development of new models and algorithms for assessing the quality of web applications.

mathematical model, quality, software, web application, normalizing transformation, nonlinear regression, software metric

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