Reliability and risk analysis under peaks over a random threshold value-at-risk method based on a new flexible skew-logistic distribution

This article introduces a new family of skew-logistic distributions called the Flexible Skew-Logistic (FSL) distribution, which can accommodate bimodal data. Key structural properties of the new distribution, including moments, moment generating function, and characteristic function, are evaluated. Additionally, various approaches are used to characterize the new model. The adaptability and usefulness of the new model are tested against other distributions using two real-life datasets. A simulation analysis is conducted to assess the performance of the MLEs of the location-scale extended density function. Based on FSL model, a risk analysis of aircraft window glass strength is developed, which is essential for ensuring safety, compliance, and reliability in aviation. It facilitates informed decision-making, enhances design optimization, and ultimately boosts the overall performance and safety of aircraft operations. To achieve this, we employed various metrics, including peaks over a random threshold value-at-risk (PORT-VaR), value-at-risk (VaR), tail value-at-risk (TVaR), and the mean of order-P (MOOP). These metrics provide insights into different aspects of tail behavior, which is crucial for understanding reliability data. Notably, PORT-VaR enhances risk assessments by incorporating randomness in threshold selection, while VaR and TVaR focus on potential losses at specific confidence levels, with TVaR offering valuable insights into significant tail risks. The MOOP method helps strike a balance between reliability objectives and performance optimization amidst uncertainty.