Abstract: In this proper we deal with a system with two components connected in series. Let the reliability of the system be R. The asymptotic beharior of Lindstrom and Maddens’ lower confidence limit \hatR_L M of R is discussed. It is proved in this paper that \hatR_L M is asymptotically equivalent to the series of the optlmal monotone confidence limits, when the confidence level is 1-α≥（1/2）.