A new non-parametric hypothesis testing with reliability analysis applications to model some real data

Due to the essential necessities of current technology and contemporary sciences, a methodical approach to investigating every occurrence or action occurring in the world was required. As a result, it makes sense that such an approach would be required in the investigation of the reliability of technological systems and products. In actuality, there are instances when system parts gradually deteriorate over time t, at which point the system needs to be updated by replacing the spare parts. Although renewal tries to improve system usability, it is unable to restore the system to its prior state. We discovered that an entirely novel domain of reliability known as classes of life distributions has emerged as a result of the growth of criteria for determining the success or failure of dependability over the previous few decades. Moreover, the other nonparametric tests of life distribution lack test efficiency and have low test power. On the other hand, based on that approach, the non-parametric statistical test utilized in this study evaluates different types of treatment by examining failure behavior in the survival data that was collected. As a result, in this ivestigation, we have developed a novel test of life distribution in this study that considers the power and effectiveness of the test. In order to compare data belonging to the harmonic new better than used in expectation (HNBUE) class with data that follow an exponential distribution, this article suggests nonparametric tests for both censored and uncensored data. The higher percentile points of the test statistics are collected, and the suggested test's normality is verified. The Pitman asymptotic relative efficiency (PARE) and powers of proposed test are calculated a few well-known alternative asymmetric models. Three asymmetric real-world data sets are examined to demonstrate the paper's findings.