A Novel Reciprocal-Weibull Model for Extreme Reliability Data: Statistical Properties, Reliability Applications, Reliability PORT-VaR and Mean of Order P Risk Analysis

Peaks over a random threshold value-at-risk (PORT-VaR) analysis is a powerful tool for evaluating extreme value reliability data, particularly for materials like carbon and glass fibers. By incorporating random thresholds into traditional value at risk (VaR) and tail value at risk (TVaR) frameworks, it provides a more nuanced understanding of how materials behave under extreme conditions, making it invaluable for applications where failure is costly or dangerous, such as aerospace, automotive, and civil engineering. The combination of Mean of Order P (MO-P), VaR and PORT-VaR analyses in medical data offers important insights into risk evaluation and patient management. By examining both average and extreme strength of glass fibers, healthcare professionals can create more effective treatment plans, enhance patient outcomes, and improve overall care quality. This comprehensive approach enables more sophisticated decision-making and targeted interventions in clinical settings. To illustrate our main objective and conduct a medical analysis, we introduced a new extreme value model called the generalized Rayleigh reciprocal-Weibull (GR-RW) and presented its key mathematical results. Additionally, we conducted a simulation study and analyzed two real datasets to compare the competing models.