In this paper, testing Ho : () ~ ()o versus HI : () < ()o for the lifetime parameter () in an
exponential distribution based on type-I censored data is studied. Certain properties associated
with φ* are addressed. We compare the performance of φ* with that of Spurrier and Wei's
(1980). The exact powers and asymptotic powers of cp* and cpsw are computed. Some local
optimality of the proposed test is also studied.