2014/05/18 by Abbas Pak, Pak, Abbas, Nayereh Bagheri Khoolenjani +3
Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST) #math.ST #stat.ME #stat.TH
paper · pdf · doi:10.48550/arxiv.1405.4529
Accepted for publication. Communications in Statistics- Theory and Methods, 2012
arxiv created 2014/05/18 · arxiv updated 2014/05/20
This paper deals with the estimation of reliability R=P(Y<X) when X is a random strength of a component subjected to a random stress Y and (X,Y) follows a bivariate Rayleigh distribution. The maximum likelihood estimator of R and its asymptotic distribution are obtained. An asymptotic confidence interval of R is constructed using the asymptotic distribution. Also, two confidence intervals are proposed based on Bootstrap method and a computational approach. Testing of the reliability based on asymptotic distribution of R is discussed. Simulation study to investigate performance of the confidence intervals and tests has been carried out. Also, a numerical example is given to illustrate the proposed approaches.