An exact and interpretable test for detecting aging behavior in reliability and survival data.

Area of Science:

• Reliability Engineering
• Survival Analysis
• Statistical Inference

Background:

• Aging behavior identification is crucial for risk assessment and system reliability.
• The exponential model is the benchmark for no aging, making departure detection a key statistical task.
• Existing methods may lack exact finite-sample validity or practical interpretability.

Purpose of the Study:

• Develop an exact nonparametric test for increasing failure rate in average (IFRA) aging.
• Provide a statistically rigorous and practically interpretable measure of departure from exponentiality.
• Offer a tool for accurate aging behavior assessment in complete lifetime data.

Main Methods:

• Constructed a test via a deviation functional from IFRA class properties.
• Derived an exact finite-sample test statistic using normalized spacings.
• Established an asymptotic normal characterization and developed a scale-invariant formulation.

Main Results:

• The proposed test provides exact finite-sample inference without asymptotic approximations.
• Monte Carlo simulations show strong empirical power against various aging models.
• The method demonstrates competitive performance compared to existing procedures.

Conclusions:

• The developed test is a statistically rigorous and practically relevant tool for detecting aging patterns.
• It combines exact finite-sample validity, asymptotic tractability, and strong empirical performance.
• The test aids in distinguishing aging systems from those with random failure rates.