On Predictive Modeling for the Al2O3 Data Using a New Statistical Model and Machine Learning Approach

Abstract

In this article, we focused on predictive modeling for real data by means of a new statistical model and applying different machine learning algorithms. The importance of statistical methods in various research fields is modeling the real data and predicting the future behavior of data. For modeling and predicting real-life data, a series of statistical models have been introduced and successfully implemented. This study introduces another novel method, namely, a new generalized exponential-X family for generating new distributions. This method is introduced by using the T-X approach with the exponential model. A special case of the new method, namely, a new generalized exponential Weibull model, is introduced. The applicability of the new method is illustrated by means of a real application related to the alumina (Al2O3) data set. Acceptance sampling plans are developed for this distribution using percentiles when the life test is truncated at the pre-assigned time. The minimum sample size needed to make sure that the required lifetime percentile is determined for a specified customer’s risk and producer’s risk simultaneously. The operating characteristic value of the sampling plans is also provided. The plan methodology is illustrated using Al2O3 fracture toughness data. Using the same data set, we implement various machine learning approaches including the support vector machine (SVR), group method of data handling (GMDH), and random forest (RF). To evaluate their forecasting performances, three statistical measures of accuracy, namely, root-mean-square error (RMSE), mean absolute error (MAE), and Akaike information criterion (AIC) are computed.