In this paper first we define log-bathtub distribution using the bathtub distribution given in Chen [7]. Then a conditional test based on quadratic form using type-2 censored sample for testing exponentiality against log-bathtub alternative is proposed. The percentile points and powers are simulated. The proposed test performs well in identifying log-bathtub alternative β < 1  even for small samples and log-bathtub alternative  β > 1 only for large samples. An example based on type-2 censoring is also discussed.

conditional test, exponentiality, log-bathtub distribution, type-2 censoring scheme, shape parameter, conditional distribution, sufficient statistic, nuisance parameter, quadratic form, percentile points, power of the test.