A new flexible power-X family of distributions: Applications to reliability engineering data

Probability distributions are crucial for representing and analyzing datasets in real-world applications, especially in the reliability engineering sector. Engineering data sets often exhibit negative skewness, positive skewness, or symmetry, requiring a flexible distribution that accommodates the characteristics of such data. In this article, we introduce a novel method of probability distributions designed to model engineering datasets effectively. The newly introduced versatile method is termed the New Flexible Power-X (NFP-X) family approach. The Weibull distribution is adopted as the base model, and a specialized sub-model of the developed approach, called the New Flexible Power Weibull (NFP-Weib) distribution, is proposed. The NFP-Weib distribution is flexible and exhibits increasing, reverse-J, decreasing, unimodal, and bathtub-shaped hazard rate functions. For the proposed family, some fundamental properties are explored in detail, and the MLE (maximum likelihood estimation) approach is employed to determine its associated parameters. A detailed simulation experiment is conducted to judge the practical effectiveness of the employed estimation method for the introduced family in terms of biases and mean square errors. Finally, three real-world datasets from the engineering sector are analyzed to evaluate the practical performance of the newly introduced family. We believe that the newly proposed NFP-X family introduces versatile models that can effectively handle both monotonic and non-monotonic data, making it particularly valuable for survival and reliability analysis.