Power law process (PLP) or Weibull process is used to model reliability growth and is usually characterized by the intensity function . We investigate the conditional confidence interval (CCI) for the ratio of two PLP shape parameters following the rejection of the hypothesis . This interval has been found to be possibly shorter than the unconditional confidence interval (UCI). The conditional coverage probability (CCP) of the confidence interval is obtained by computing the coverage probability under the conditional probability density function. The CCP of the UCI is not uniformly greater than or less than the nominal level. The UCI is appropriate only when one does not perform any preliminary test (pre-test). However, if a pre-test is performed before the construction of a confidence interval, then the appropriate interval is the CCI as the pre-test affects subsequent inference procedures. The method is illustrated on a data set.