On the mean residual life order of convolutions of independent uniform random variables

Let X λ i , i = 1 , … , n be n independent random variables such that X λ i has uniform distribution over the interval ( 0 , 1 / λ i ) , i = 1 , … , n . It is proved that if ( λ 1 , … , λ n ) is larger than ( λ 1 ⁎ , … , λ n ⁎ ) according to reciprocal order, then ∑ i = 1 n X λ i is larger than ∑ i = 1 n X λ i ⁎ according to mean residual life order as well as increasing convex order. This result gives convenient bounds for mean residual life function of ∑ i = 1 n X λ i in terms of harmonic mean of λ i ʹs. It is shown that these bounds are sharper than those given in the literature in terms of geometric mean and arithmetic mean of λ i ʹs.