Development and Characterization of a New Linear Exponential Distribution for Reliability Analysis of Complex Systems
Keywords:
Linear Exponential Distribution; Reliability Analysis; Complex Systems; Hazard Function; Lifetime Data; Generalised Linear Exponential Distribution (GLED); Statistical Modeling; Failure Time; Survival Function; Engineering ReliabilityAbstract
The increasing demand for precise reliability modeling in complex systems, such as aerospace structures, nuclear facilities, and biomedical devices, necessitates the development of robust statistical tools. This study introduces a novel extension of the linear exponential distribution tailored specifically for reliability analysis of complex systems, where traditional models often fail to accommodate the varying hazard rates encountered in real-life operations. By embedding a shape parameter that adapts to increasing or decreasing failure rates, the proposed Generalised Linear Exponential Distribution (GLED) offers higher flexibility and accuracy in modeling lifetime data. The theoretical formulation is rigorously derived, and properties such as moment generating functions, hazard functions, and survival functions are analytically characterized. The distribution is evaluated using real-world reliability datasets from NASA’s Jet Propulsion Laboratory and the IEEE Reliability Society. Comparative performance analysis with classical exponential and Weibull models is conducted through Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), and mean square error (MSE) metrics. Results show that the proposed model significantly improves predictive accuracy in failure time modeling. This advancement contributes not only to statistical theory but also offers immediate practical applications in designing safer and more reliable systems.
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