Abstract: In this paper, R_L、C_uandK_u, the Conditional UMA （uniformly most accurate） r upper （Lower） confidence limits for the normal one-sided reliability R, the coefficient of variation C for normal distribution and exponential environmental factor K, are given. It is pointed out that: 1. the R_L are equal to Bayesian lower limits taking right invariant Haar prior measure and Fiducial lower limits of R. 2. the K_u are equal to Bayesian upper limits taking invariant Haar prior measure and Fiducial upper limits of K..