This thesis is concerned with estimating the probability that at least s out of k exponential random variables are greater than another exponential random variable with Type II censoring.
Maximum likelihood estimator (MLE) and uniformly minimum variance unbiased estimator (UMVUE) of the probability are obtained. Bayes estimators are also obtained under noninformative prior and gamma conjugate prior distributions for the parameters involved. The asymptotic behaviors of MLE are examined and the asymptotic equivalence with UMVUE and Bayes estimators is shown. Performance of the three estimators for moderate sample sizes is studied by Monte Carlo simulation. Tests of some hypotheses for the probability are also considered.