The lifetime performance index \(C_{L}\) measures the performance of a process in terms of the lifetime of produced items. In this article, we use the fiducial approach to estimate the lower confidence bound of the lifetime performance index under some location-scale distributions. We consider three important lifetime distributions: two-parameter exponential, two-parameter Rayleigh and Weibull distribution. Often lifetime data comes as censored data instead of complete data. Here we consider type-II censored samples. The fiducial quantities are estimated based on the MLE. The performance of our proposed lower confidence bound using fiducial approach is compared with some existing lower confidence bound in terms of their coverage probability and average value. It is observed through the discussion that the overall performance of our proposed lower confidence bound is better than the existing lower confidence bounds. Hence the proposed method estimates a very reliable confidence bound. An example is given to illustrate the applicability of our proposed lower confidence bound in industry.
