Estimation on the lower confidence limit of the breaking strength percentiles under progressive type-II censoring

The breaking strength information of structure components is highly correlated with the safety manufacturing and much concerned by engineers. Components with deficient safety quality will be rejected to rework or discard due to an unsatisfactory level of the lower critical breaking strength percentile. When the breaking strength of components is assumed to have a Burr type-XII distribution, five parametric bootstrap methods are suggested to adjust the bias of the lower confidence limit estimate of the lower percentile with progressive type-II censored samples. The performance of the proposed bootstrap methods is evaluated through an intensive simulation study. Numerical results show that the hybrid bootstrap method and the bias-corrected and accelerated bias-corrected methods perform better with coverage probabilities near the nominal confidence level for almost all the cases considered. An example of the breaking strength data set of aluminum sheets is used for illustration.