An Entropy-Based Scale-Free L-Statistic for Exponentiality Testing in Lifetime Data with DMRL Aging

Area of Science:

• Reliability Engineering
• Statistical Inference
• Survival Analysis

Background:

• Lifetime data analysis is crucial for understanding product lifespan and failure patterns.
• The decreasing mean residual life (DMRL) aging class is a key characteristic in reliability studies.
• Existing methods for DMRL testing may lack scale invariance or entropy-based foundations.

Purpose of the Study:

• To develop a novel entropy-based scale-free L-statistic for testing exponentiality against DMRL alternatives.
• To provide a statistical tool that quantifies deviations from the exponential distribution's constant mean residual life property.
• To assess the performance of the proposed test in terms of significance level and power.

Main Methods:

• Derivation of a scale-free L-statistic from a mean-residual-life characterization and cumulative residual entropy.
• Normalization of the statistic by the sample mean to achieve scale invariance.
• Determination of the exact null distribution using normalized spacings and establishment of asymptotic normality.

Main Results:

• The proposed entropy-based L-statistic provides a scale-invariant test for exponentiality under DMRL.
• Simulations demonstrate that the test maintains the nominal significance level across various DMRL alternatives.
• The test exhibits competitive power compared to existing DMRL procedures in simulation studies.

Conclusions:

• The developed entropy-based scale-free L-statistic is a valuable tool for detecting DMRL aging in lifetime data.
• The method offers a robust and statistically sound approach for reliability and survival data analysis.
• Real-data applications confirm the practical utility of the proposed statistical method.