This paper proposes a simple goodness-of-fit test based on the sample covariance. It is shown that this test is preferable for alternatives of increasing and unimodal failure rate. Critical values for various sample sizes are determined by means of Monte Carlo simulations.

We compare the test based on the sample covariance with tests based on Hoeffding's maximum correlation. The usefulness of the proposed test is shown for a real example.

An empirical power study shows that the new test has the same level or upper level of performance than the best exponentiality tests in the statistical literature.