The log-linear failure rate distribution: properties, estimation and application to aircraft windshield failure and service data

Abstract

This study proposes the Log-Linear Failure Rate (Log-LFR) distribution, a novel extension of the classical Linear Failure Rate model achieved through a logarithmic transformation. The suggested logarithmic generator is characterized by its survival-based construction, permitting a natural hazard interpretation and an effortless recovery of the baseline model as the logarithmic parameter tends to one. It improves tail flexibility and accommodates various hazard behaviors while preserving analytical flexibility and symmetry. While several extensions of the Linear Failure Rate distribution exist, the logarithmic transformation has not been explored before. This addresses a gap in the literature and provides more flexibility in modeling diverse aging patterns and failure behaviors. We investigate the statistical and reliability properties of the proposed Log-LFR distribution such as moments, moment generating function, quantile function, order statistics and reliability measures. Further, stochastic comparisons are studied under sufficient conditions to provide theoretical insights into the distribution’s behavior. Parameters are estimated using Maximum Likelihood Estimation. Their performance is validated through extensive Monte Carlo simulations showing accuracy and robustness. The model is applied to two real-world datasets on aircraft windshield failure and service times. In both instances, it shows a better fit than other competing models. These results show the Log-LFR distribution as a versatile and effective tool for reliability and survival data analysis in industrial and aerospace applications.