A Novel Statistical Test for Life Distribution Analysis: Assessing Exponentiality Against EBUCL Class with Applications in Sustainability and Reliability Data

Abstract

A product’s lifespan may be ascertained by analyzing the dependability and aging class of its life distribution. Sustainability metrics are also crucial for assessing the impact on the environment and creating resource-saving strategies. Researchers extensively rely on statistical testing when making judgments; nonparametric tests are particularly useful, since they may be used for a broad variety of datasets and do not require knowledge of the data distribution. To provide effective assessments for well-informed decisions, this study introduces a novel life distribution class called “Exponential Better than Used in Increasing Convex in Laplace Transform Order (EBUCL)”. In this framework, a novel test statistic utilizing the moment inequalities method is introduced to evaluate exponentiality against the EBUCL class. By analyzing its asymptotic behavior, critical values are calculated for sample sizes between 5 and 100. Pitman’s asymptotic efficiency was taken into consideration by calculating the test’s power and comparing it with other tests through the use of simulation studies employing standard reliability distributions. In conclusion, this study addresses the treatment of right-censored data and applied the suggested test approach to real datasets across many domains. Our experimental results have practical implications for sustainability data assessments in engineering and the biological sciences.