Abstract
The estimation of mean lifetimes in presence of interval censoring with mixed replacement procedure are examined when the distribution s of lifetimes are exponential. it is assumed that due to physical restrictions and/or economic constraints the number of failures is investigated only at several inspection times during the lifetime test; thus there is interval censoring. Comparisons of mixed replacement designs are made with those with and without replacement The maximum likelihood estimator is found in an implicit form. The Cramer-Rao lower bound which is the asymptotic variance of the estimator is derived. The test conditions for minimizing the Cramer-Rao lower bound and minimizing the test costs within a desired width of the Cramer-Rao bound have been studied.