  Hazard rates play an important role in various areas, e.g., reliability
theory, survival analysis, biostatistics, queueing theory and actuarial
studies. Mixtures of distributions are also of a great preeminence in such
areas as most populations of components are indeed heterogeneous. In this study
we present a sufficient condition for mixtures of two elements\ of the same
natural exponential family (NEF) to have an increasing hazard rate. We then
apply this condition to some classical NEF's having either quadratic, or cubic
variance functions (VF) and others as well. A particular attention is devoted
to the hyperbolic cosine NEF having a quadratic VF, the Ressel NEF having a
cubic VF and to the Kummer distributions of type 2 NEF. The application of such
a sufficient condition is quite intricate and cumbersome, in particular when
applied to the latter three NEF's. Various lemmas and propositions are needed
then to verify this condition for these NEF's.
