Sharp bounds for NBUE distributions

Abstract

Let F be a new better than used in expectation (NBUE) distribution function with mean μ. In a previous paper (Brown in Probab. Eng. Inf. Sci. 20:195–230, 2006), the author derived the following bound. For any t≥μ, $$\overline{F}(t) = \mathit{Pr}(X \ge t) \le e^{-[{t\over\mu}-1]}. $$ The main result of this paper is to show that this bound is sharp. Other sharp bounds for NBUE distributions are also derived.