  Suppose F and G are two life distribution functions. It is said that F is
more IFRA than G (written by F<_* G) if G^(-1) F(x) is starshaped on (0,infty).
In this paper, the problem of testing H_0:F=_* G against H_1:F<_* G and F
\neq_* G is considered in both cases when G is known and when G is unknown. We
propose a new test based on U-statistics and obtain the asymptotic distribution
of the test statistics. The new test is compared with some well known tests in
the literature. In addition, we apply our test to a real data set in the
context of reliability.
