A Novel Nonparametric Approach to Modeling Lifelength Distributions and Aging Processes

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In this article, we present a novel nonparametric class of life distributions, using the concept of starshaped functions, to address challenges encountered in reliability and life testing. Our focus is on scenarios where the increasing or decreasing Mean Residual Life (IMRL or DMRL) aging classes prove inadequate in capturing the underlying aging process. Motivated by practical challenges in applied reliability, we introduce a test procedure designed to assess whether the overall remaining life distribution exhibits a decreasing Mean Residual Life (MRL) property, specifically concerning the exponential distribution.The proposed test accommodates right-censored and randomly censored data as well. We conduct simulation studies to evaluate the empirical power of the test. This work aims to provide a valuable tool for modeling aging processes in situations where the IMRL concept falls short, but overall lifelengths demonstrate improvement with age. We believe that our approach contributes to the broader understanding of reliability analysis and life testing, addressing gaps left by traditional aging classes.

Starshaped function

Renewal Process

U-statistics

Equilibrium distribution

Mean residual life distribution

Stochastic process 

Section on Nonparametric Statistics