Statistical modeling of reliability functions and their applications in engineering

Abstract

Reliability analysis is a critical component of engineering systems, ensuring the safe
and efficient operation of components under specified conditions. This paper presents a rigorous
mathematical framework for modeling reliability functions using statistical methods. We explore key
reliability models such as the exponential, Weibull, and lognormal distributions, and demonstrate
their application in predicting failure rates, optimizing maintenance schedules, and enhancing
system performance. The results are supported by parameter estimates, graphical representations,
and comparative analyses. Our findings highlight the importance of advanced probabilistic models
in addressing real-world engineering challenges.