Reliability Estimation after Selection from one Parameter Exponential Population Ajaya Kumar Mahapatra1*- 1Centre for Applied Mathematics and Computing, Siksha O Anusandhan University, Bhubaneswar-751030, India. Brijesh Kumar Jha2 - 2Department of Mathema

Abstract

Let ?1,?2,...,?k be k populations, where ?i being exponential with unknown hazard rate ?i, i =1,...,k.  Suppose independent random samples are drawn from populations ?1,?2,...,?k.  Let Xi1,Xi2,...,Xin, i =1,...,k. be a random sample of size n drawn from the ithpopulation.  Let Xi = ?_(j=1)^n?X_ij be the sample mean of  ithpopulation. The natural selection rule is to select the population with the highest mean.  That is, ?i is selected, if Xi = max(X1, . . . ,Xk ). We consider the problem of estimating the Reliability function of the selected population. The Unique Minimum Variance Unbiased Estimator(UMVUE) is derived and some natural estimators are proposed. Finally a numerical comparison of the risks of these estimators is done when the loss function is squared error.