Approximately optimum confidence bounds on series system reliability for exponential time to failure data

For a series system with exponentially distributed survival times for independent subsystems, there exist optimum uniformly most accurate unbiased exact confidence bounds on the probability of system survival until a specified time; see Lentner & Buehler (1963) and the doctoral dissertation of A. H. El Mawaziny. Calculation of these optimum exact confidence bounds, however, must be performed iteratively by means of a high-speed computer. Moreover, their calculation can be extremely expensive in terms of computer time, and in certain cases there are serious problems of loss of precision as the number of subsystems increases. An approximation is derived which can, if necessary, be evaluated by hand and which agrees with the optimum lower confidence bound on the probability of system survival to within about a unit in the second decimal place in the many and varied cases examined. Numerical examples are given and comparisons made with other approximate confidence bounds.