ESTIMATION AND TESTING IN AN IMPERFECT-INSPECTION MODEL

An imperfect-inspection model in which failures can only be detected w ith probability beta, is considered in this paper. The lifetimes of al l the components are i.i.d. exponential with rate lambda. Using the ap proximate likelihood filtering method, a first order binomial autoregr essive model is obtained when 1 - beta is small. When lambda is known, a locally most powerful test is proposed for testing the hypothesis t hat beta = 1 against the alternative that beta < 1. The asymptotic dis tribution of the test statistic is obtained under the null hypothesis as well as under the alternative. The test statistic is modified to ha ndle the case of unknown lambda. Its asymptotic distribution is also g iven. Finally, the bias of the maximum likelihood estimators of beta & lambda obtained from the approximated likelihood function is studied by simulation.