A novel Compound-Pareto model with applications and reliability peaks above a random threshold value at risk analysis.

This paper aims to model the bimodal and right-skewed aircraft windshield data using a novel compounded-Pareto distribution. The method of maximum likelihood is employed to estimate the unknown model parameters, and the performance of the estimators under finite samples is evaluated through a comprehensive simulation study. The practical applicability of the proposed model is demonstrated using two real-world reliability datasets. Reliability analysis based on Peaks Over a Random Threshold Value at Risk (PORT-VAR) is crucial for aircraft windshield manufacturers, as it provides a rigorous assessment of extreme failure events and service times-key factors in ensuring product safety and longevity. By identifying the frequency and severity of failures exceeding specific VAR thresholds, this analysis enables companies to understand the upper bounds of their products' performance under stress, optimize designs for enhanced durability, and develop proactive maintenance strategies. In this paper, we present a comprehensive reliability PORT-VAR analysis to support these objectives and highlight the relevance of the proposed model in extreme value risk modeling and real-world reliability scenarios.