In this article, bootstrap and Shewhart type process control monitoring schemes are proposed for the quantiles of generalized Weibull distribution under hybrid censoring. Monitoring schemes for the quantiles of Weibull, generalized exponential, Rayleigh, and Burr type $X$ distributions for type I, type II and hybrid censoring can be obtained as the special cases of the proposed schemes. The maximum likelihood estimators are derived under hybrid censoring using EM algorithm and the asymptotic properties of the estimators are discussed in order to develop the Shewhart type scheme. The in-control performance of the schemes is examined in a simulation study on the basis of the average run length for different choices of quantiles, false-alarm rates and sample sizes. Behavior of the out-of-control performance of the schemes is studied for several choices of shifts in the parameters of the chosen density function. The proposed monitoring schemes are illustrated with an example from healthcare and compared with similar schemes under type I and type II censoring. The schemes are found to detect out-of-control signals effectively in terms of frequency and speed both.

翻译：本文提出了针对混合删失下广义威布尔分布分位数的Bootstrap型与Shewhart型过程控制监控方案。对于I型、II型及混合删失条件下威布尔分布、广义指数分布、瑞利分布以及Burr型X分布分位数的监控方案，均可作为所提方案的特例。采用EM算法推导了混合删失下的极大似然估计量，并讨论了估计量的渐近性质以建立Shewhart型监控方案。通过模拟研究，基于不同分位数选择、误报率及样本容量下的平均运行长度，检验了方案的在控性能。针对所选密度函数参数发生多种偏移的情况，研究了方案的失控性能表现。以医疗健康领域的数据为例对所提监控方案进行了说明，并与I型及II型删失下的类似方案进行了比较。结果表明，所提方案在信号检测的频率与速度两方面均能有效识别失控信号。