This study examines the estimation of stress-strength reliability in a linearly consecutive k-out-of-n:G system, where the stress and strength variables follow to the standard omega distribution. Reliability is evaluated using classical and Bayesian methods under scenarios where the common scale parameter ( \({\theta }\) ) is either known or unknown. For the case of unknown \({\theta }\) , a unique maximum likelihood (ML) estimator of system reliability is developed. For the case of known \({\theta }\) , in addition to the ML estimator, the uniform minimum variance unbiased (UMVU) estimator of system reliability is obtained. Furthermore, Bayesian reliability estimates are computed using techniques such as Markov chain Monte Carlo (MCMC), Tierney–Kadane approximation, Lindley’s approximation, and exact methods. The study also includes the asymptotic confidence interval and the highest posterior density credible interval for system reliability. A Monte Carlo simulation study evaluates the performance of these estimators, supplemented by real data analysis to demonstrate practical applications.
