Monitoring the inverted exponentiated half logistic quantiles under the adaptive progressive type II hybrid censoring scheme.

Numerous studies have solved the problem of monitoring statistical processes with complete samples. However, censored or incomplete samples are commonly encountered due to constraints such as time and cost. Adaptive progressive Type II hybrid censoring is a novel method with the advantages of saving time and improving efficiency. On the basis of this scheme, the problem of monitoring a downward shift in the quantiles of the inverted exponentiated half logistic distribution is considered. The conventional Shewhart control chart is insensitive to detect quantile shifts from faulty data processes that exhibit deviations from normality or symmetry. To overcome this limitation, Bootstrap control charts combining with the exponentially weighted moving average method based on the Bayesian estimation and maximum likelihood estimation are proposed, respectively. They are compared with the conventional Shewhart control chart via average run length through Monte-Carlo simulations. Finally, a real dataset related to the tensile strength of carbon fibers is employed to demonstrate the ascendancy of the Bootstrap control charts.