Statistical inference about the shape parameter of the Burr type XII distribution under the failure-censored sampling plan

In this paper, we propose m pivotal quantities to test the shape parameter and establish confidence interval of the shape parameter of the two-parameter Burr type XII distribution under the failure-censored plan (see [J. Statist. Comput. Simul. 52 (1995) 337]). Next, we find the best test statistic based on their most power of test among all test statistics. Moreover, we also obtain the best pivotal quantities with the shortest tolerance length. 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.