(untitled) (Contemporary Mathematics, 2024)
The purpose of this study is to determine the relationship between the values and attributes of the loads in forged rings made of materials such as nickel, titanium and waspaloy in furnaces for their heat treatment and a prediction model on the preparation and temperature stabilization time of the furnaces, and to be able to carry out the loads and start their holding time according to the recipe assigned for their heat treatment. Applying the Factorial Analysis method, it is possible to identify a reduced number of significant factors that can represent the relationship of the independent variables set, as well as a Multiple Regression Analysis and Random Forest that allows establishing an estimation or prediction system for the time it takes for the furnace to operate the preheating and receive the scheduled load. 6,135 data were collected from full loads in 2020 and six months of 2021, the results had a total variance of 64.61%, a Kaiser-Meyer-Olkin index of 0.620 and a Bartlett sphericity test with a significance of 0.00. The study significantly identifies three important factors on the preparation time of furnaces obtained from the factor analysis, which are: the conditions between loads that represent 33.203% of the total variance, the temperature accuracy for the load 18.149% and the exposure of material in furnaces 13.263%. From the factors identified in the Multiple Regression and Random Forest analysis, it was obtained that the relevant variables are: the temperature difference with respect to the previous load, the weight of the load, the time of holding the load and the treatment temperature for its maintenance have a significant impact on the preparation time. The best prediction method is through the Random Forest algorithm, explaining 95.11% of the variability, its accuracy with respect to the mean square error (MSE) is 6.94 minutes, a mean absolute percentage error (MAPE) of 3.1%, while Multiple Regression manages to explain 77.5% of the variability, a MSE of 69.25 minutes and a MAPE of 9.4%. The result of this research benefits programmers to formulate load sequencing more efficiently in the heat treatment area using the Random Forest algorithm, allowing to increase the productivity and utilization of the furnaces.