When the sampling distribution of a parameter estimator is unknown, using normality asymptotically, the Shewhart-type chart may provide improper control limits. To monitor Burr type-X percentiles, two parametric bootstrap charts (PBCs) are proposed and compared with the Shewhart-type chart via a Monte Carlo simulation. Simulation results exhibit that the proposed PBCs perform well with a short average run length to signal out-of-control when the process is out-of-control, and have more adequate control limits than the Shewhart-type chart in view of in-control false alarm rate. An example regarding single fiber strength is presented for illustrating the proposed PBCs.
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Lio et al. (2013) studied this question.