Estimation of multicomponent stress-strength reliability based on a bivariate Topp-Leone distribution

In this endeavour, we study the statistical inference of multicomponent stress-strength reliability when components of the system have two paired elements experiencing common random stress. The k strength variables (X-1, Y-1), ... , (X-k, Y-k) follow a bivariate Topp-Leone distribution and the stress variable which follows a Topp-Leone distribution. This system is unfailing when at least s(1 <= s <= k) out of k components simultaneously activate. The maximum likelihood estimate along with its asymptotic confidence interval, the uniformly minimum variance unbiased estimate, and the exact Bayes estimate of stress-strength reliability are derived. Further, we determined the Bayes estimates of the stress-strength reliability via different methods such as the Tierney and Kadane approximation, Lindley's approximation, and the Markov Chain Monte Carlo (MCMC) method, to compare their performances with the exact Bayes estimate. Also, the highest probability density credible interval is obtained using the MCMC method. Monte Carlo simulations are implemented to compare the different suggested methods. Ultimately, the analysis of one real data is investigated for illustrative purposes.