Análise de regressão linear e análise de capacidade aplicadas a dados industriais de aços API X42Q e X60Q

Abstract

In industrial activities, the application of statistical methods to control and improve processes was, and still is, extremely important for obtaining superior results in production processes. This work aims to demonstrate how the application of statistical data analysis methods can contribute to understanding the behavior of product and process control variables, allowing action on variables of greater statistical significance for day-to-day management in companies. Through the analysis of an industrial database, and the application of multiple linear regression techniques, we sought to evaluate the different product and process variables that impact the resistance of API 5L class steels Grades X42Q and X60Q. Various statistical techniques were applied to measure the relative importance of items of chemical composition of the alloy, the presence of process deviations in the heat treatment times of steels (excessive treatment times). Process capacity analysis techniques were carried out, with a view to verifying the level of compliance with the applicable standard specifications of both steels. Techniques for choosing linear models were applied to obtain a regression equation that is meaningful for the study of the production process of the chosen grades of API 5L steels. In order to verify the adequacy of the final regressive model chosen, model residue analysis techniques were applied to verify the normality of the data, and for the selection of the final model and choice between two final models obtained in linear regression, techniques were used to choose models and perform the calculations of indices such as the PRESS statistic, Mallows Cp, AIC (Akaike Information Criterion), in addition to the analysis of the mean square of residuals (QMRES) and analysis of the presence of multicollinearity through the calculation of the Variance statistic Inflation Factor (VIF). For the final model chosen, the presence of autocorrelation in the residues was verified using the Durbin-Watson test, and for the homogeneity of variances, the Breusch-Pagan test was performed, with the respective hypothesis tests confirming that there was significant statistical evidence. of the presence of both autocorrelation and heteroscedasticity of the residuals, requiring further complementary analyzes in future work to better understand the causes that led to the rejection of the aforementioned tests. The use of capacity analysis and linear regression techniques were useful and important for understanding the production process of API 5L Grades X42Q and X60Q steels, verifying the ability to meet applicable standards, as well as differentiating the steels in a comparative manner between its technical specifications, in addition to indicating the relative importance of the process variables adopted for linear regression and its controls for the company's production process.