Estimation of Multicomponent System Reliability for a Bivariate Generalized Rayleigh Distribution

The study of a multicompnent system with k identical components which are independent to each other is considered in the present work. The components of the system have series structure with two dependent elements that are exposed to a common random stress. Here, strength vectors follow bivariate generalized Rayleigh distribution and a common random stress follow generalized Rayleigh distribution. The s-out-of-k system is said to function if atleast s out of k(1 ≤ s ≤ k) strength variables exceed the random stress. The estimation of system reliability is studied using maximum likelihood and Bayesian approaches. The maximum likelihood estimates are derived under simple random sampling and ranked set sampling schemes. The approximate Bayes estimates for system reliability are obtained using Lindley's approximation technique. Simulation study is conducted to study the performance of the estimators of reliability using mean squares error criteria.