Evaluations of the mean residual lifetime of an m-out-of-n system

The mean residual lifetime is an important measure in the reliability theory and in studying the lifetime of a living organism. This paper presents sharp upper bounds on the deviations of the mean residual lifetime of an m-out-of-n system from the mean of a residual life random variable Xt=(X−t|X>t), for any arbitrary t>0 in various scale units generated by central absolute moments. The results are derived by using the greatest convex minorant approximation combined with the Hölder inequality. We also determine the distributions for which the bounds are attained. The optimal bounds are numerically evaluated and compared with other classical rough bounds.