*Result*: On the use of a new probabilistic model and machine learning methods with applications to reliability and music engineering.

*In this paper, we considered a new probability distribution with new applications in the field of engineering, in particular, in music engineering. The new probability distribution is mainly based on the Weibull distribution and cosine function. We call this the weighted cosine flexible Weibull distribution. The point estimators for the new distribution are obtained. We evaluate these point estimators for three sets of parameter values. The illustration of the weighted cosine flexible Weibull distribution is provided for two practical data set which are drawn from the reliability and music engineering. In addition, to dual robust machine learning approaches, we implement the Lasso (Least Absolute Shrinkage and Selection Operator) and Elastic Net (ENet) to improve the predictive performance of the data. This was done in response to the existence of outliers in the same datasets. We provide comparative analysis to see how well these approaches performed in comparison to the Step Indicator Saturation (SIS) method. [ABSTRACT FROM AUTHOR]*