This study is a first step towards a comprehensive analysis of the effects of parameter estimation on the monitoring of autocorrelated count processes. Focusing on Shewhart’s c and np charts, various types of count process with different dispersion properties and model structures are considered. The pure effect of discreteness of observations is contrasted with the additional consequences of estimation uncertainty on the control limits of the charts as well as on the resulting run length performance. The main parameter regarding a trustworthy chart design is the actual dispersion of the count process, which, in turn, might be connected to the extent of serial dependence for certain types of process. For some low-dispersion scenarios, the effect of parameter estimation on the design parameters might even fully vanish. The acquired results are illustrated with two real-data examples, where a parametric bootstrap approach is used to judge the reliability of the obtained chart design.

这项研究是全面分析参数估计对自动相关计数过程的监视效果的第一步。专注于Shewhart的c和np图表，考虑了具有不同分散特性和模型结构的各种计数过程。观测值离散的纯粹影响与估计不确定性对图表控制范围以及最终行程长度性能的其他影响形成对比。有关可信赖的图表设计的主要参数是计数过程的实际分散度，而这又可能与某些类型的过程的序列依赖性程度有关。对于某些低色散方案，参数估计对设计参数的影响甚至可能完全消失。通过两个真实数据示例说明了获取的结果，其中使用了参数自举方法来判断所获得图表设计的可靠性。