A note on stochastic ordering of estimators of exponential reliability

Recently Balakrishnan and Iliopoulos [Ann. Inst. Statist. Math. 61 (2009)] gave sufficient conditions under which maximum likelihood estimator (MLE) is stochastically increasing. In this paper we study test plans which are not considered there and we prove that MLEs for those plans are also stochastic ordered. We also give some applications to the estimation of reliability.