<p>In this paper, we propose control charts to monitor quantiles of Weibull distribution for Type-I generalized hybrid censoring scheme and Type-II progressive censoring scheme. Parametric bootstrap method is employed to derive the control limits. Monte Carlo simulations are carried out to assess the in-control and out-of-control performance of the proposed charts. The phase-I analysis evaluates the performance of the charts through average run lengths for various combinations of quantile, false-alarm rate, sample size, and censoring parameters. Chart performance is thoroughly investigated in the phase-II analysis for several choices of shifts in the scale and shape parameters of Weibull distribution along with different censoring schemes. The charts for both censoring schemes have been demonstrated to be highly effective in detecting out-of-control signals, both in terms of magnitude and speed. The proposed charts are illustrated through applications in reliability and clinical practices. While both charts show similar performance in terms of speed, the chart with the optimal Type-II progressive censoring scheme outperforms the one with the Type-I generalized hybrid censoring scheme in terms of magnitude in both examples.</p>