The significance of probability distributions in representing practical occurrences cannot be overstated. In particular, the two-parameter Weibull distribution and the inverse Weibull (I-Weibull) distribution have proven to be highly effective in various engineering applications. This research focuses on the evolution and practical implications of a newly modified version of the I-Weibull distribution. The modification introduced is referred to as the sine cosine inverse Weibull (SCI-Weibull) distribution. We offer an in-depth examination of the mathematical characteristics of the SCI-Weibull distribution, with particular emphasis on its properties related to quartiles. The methodology for estimating the parameters, along with simulation studies for various combinations of parameter values, is also discussed. An illustrative case from the field of music engineering, showcasing the lifespan of headphones, has been selected to substantiate the superiority of the SCI-Weibull distribution. Moreover, the study examined two machine learning algorithms, k-Nearest Neighbors (KNN) and artificial neural network (ANN), for the purpose of predicting headphone lifespan. The results revealed that ANN was more adept at capturing noise present in musical data than KNN. This phenomenon can be regarded as a capacity of the ANN to comprehend the complex and non-linear relationships patterns within the musical data.