Abstract
If two censored samples come from the exponential distributions with identical scale parameters, it is advantageous to pool the two samples to construct a confidence interval for the scale parameter. In practice, when it is uncertain whether these two samples come from the distributions with identical scale parameters, a preliminary test may be used to partially resolve the uncertainty. A confidence interval for the scale parameter following a preliminary test concerning the equality of scale parameters is investigated. This interval is referred to as a pre-test confidence interval. The expected length of the pre-test confidence interval is shorter than that of the usual confidence interval. The coverage probability of the pre-test confidence interval is less than the nominal level. However, at some selected levels of significance, the coverage probability of the pre-test confidence interval is only slightly less than the nominal level but the maximum reduction in expected length is substantial.
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