The parameter being estimated by using UMAU confidence interval, this method can describe precision by making an interval, which includes the smaller probability of wrong value .That is to say , when the true value of parameter is θ and unequal with θ′, Pθ(θ(X)≤θ′≤θ(X))should be small.The interval length was considered by a more direct method to describe precision, giving the conception of possessing uniformly minimum mean length confidence interval (the best confidence interval).The equivalence of two different confidence intervals was posed by some correlative knowledge .The theory of the best interval estimation is improved , which provides the theory base for application , such as studying about the best confidence interval estimation of failure rate parameters proportion on censored data .