Statistical Inference about the Shape Parameter of the Bathtub-Shaped Distribution under the Failure-Censored Sampling Plan

In this paper, we first provide m pivotal quantities to test the shape parameter and establish confidence interval of the shape parameter of the bathtub-shaped distribution under the failure-censored plan (see Balasooriya (1995) and Wu and Tsai (2000)). Next, we also find the best test statistic based on their most power of test among all test statistics and the best pivotal quantities with the shortest tolerance length, respectively. Finally, we give two examples and the Monte Carlo simulation to assess the behavior (including higher power and more shorter length of confidence interval) of these pivotal quantities for testing null hypotheses under given significance level and establishing confidence interval of the shape parameter under the given confidence coefficient.