Probability distributions have prominent applications in different sectors. Among these sectors, probability models are mostly used to analyze datasets in engineering. Among the existing probability distributions, the two-parameter Weibull model plays an important role in providing the best fit for engineering and other related datasets. This paper introduces a new method called a novel updated-W (denoted by “NU-W”) family of distributions that is used to develop a new updated form of the Weibull distribution. The proposed updated extension of the Weibull model is referred to as a novel updated Weibull (denoted as NU-Weibull) distribution. Distributional properties such as identifiability, heavy-tailed characteristic, and rth moment of the NU-W family are derived. The residual life analysis of the NU-Weibull distribution is provided. Finally, two physical applications from civil engineering and reliability sectors are analyzed to demonstrate the application and effectiveness of the NU-Weibull distribution. The data fitting results show that the NU-Weibull distribution is a more suitable and best fit for engineering datasets.

This study presents an analysis and evaluation of gait asymmetry (GA) based on the temporal gait parameters identified using a portable gait event detection system, placed on the lateral side of the shank of both lower extremities of the participants. Assessment of GA was carried out with seven control subjects (CS), one transfemoral amputee (TFA) and one transtibial amputee (TTA) while walking at different speeds on overground (OG) and treadmill (TM). Gait cycle duration (GCD), stance phase duration (SPD), swing phase duration (SwPD), and the sub-phases of the gait cycle (GC) such as Loading-Response (LR), Foot-Flat (FF), and Push-Off (PO), Swing-1 (SW-1) and Swing-2 (SW-2) were evaluated. The results revealed that GCD showed less asymmetry as compared to other temporal parameters in both groups. A significant difference (p < 0.05) was observed between the groups for SPD and SwPD with lower limb amputees (LLA) having a longer stance and shorter swing phase for their intact side compared to their amputated side, resulting, large GA for TFA compared to CS and TTA. The findings could potentially contribute towards a better understanding of gait characteristics in LLA and provide a guide in the design and control of lower limb prosthetics/orthotics.

It is proven evidently that probability distributions have a significant role in data modeling for decision-making. Due to the indispensable role of probability distributions for data modeling in applied fields, a series of probability distributions have been introduced and implemented. However, most newly developed probability distributions involve between one and eight additional parameters. Sometimes the additional parameters lead to re-parametrization problems. Therefore, the development of new probability distributions without additional parameters is an interesting research topic. In this paper, we study a new probabilistic method without incorporating any additional parameters. The proposed approach is based on a tangent function and may be called a new tangent-G (NT-G) family of distributions. Certain properties of the NT-G distributions are derived. Based on the NT-G method, a new flexible probability distribution called a new tangent flexible Weibull (NTF-Weibull) distribution is studied. The parameters of the NTF-Weibull distribution are estimated using seven different estimation methods. Based on these eight estimations, a brief simulation of the NTF-Weibull distribution is also provided. Finally, we prove the applicability of the NTF-Weibull distribution by analyzing two waiting-time data sets taken from the reliability sector. We consider three statistical tests with a p-value to evaluate the performance and goodness of fit of the NTF-Weibull distribution.