On the method of pivoting the CDF for exact confidence intervals with illustration for exponential mean under life-test with time constraints

Two requirements for pivoting a cumulative distribution function (CDF) in order to construct exact confidence intervals or bounds for a real-valued parameter θ are the monotonicity of this CDF with respect to θ and the existence of solutions of some pertinent equations for θ. The second requirement is not fulfilled by the CDF of the maximum likelihood estimator of the exponential scale parameter when the data come from some life-testing …