Shongwe Sandile Charles, Malela-Majika Jean-Claude, Castagliola Philippe
Department of Statistics, College of Science, Engineering and Technology, University of South Africa, Pretoria, South Africa.
Département Qualité Logistique Industrielle et Organisation, Université de Nantes & LS2N UMR CNRS 6004, Nantes, France.
J Appl Stat. 2020 May 4;48(7):1243-1268. doi: 10.1080/02664763.2020.1759033. eCollection 2021.
In order to reduce the effect of autocorrelation on the monitoring scheme, a new sampling strategy is proposed to form rational subgroup samples of size . It requires sampling to be done such that: (i) observations from two consecutive samples are merged, and (ii) some consecutive observations are skipped before sampling. This technique which is a generalized version of the mixed samples strategy is shown to yield a better reduction of the negative effect of autocorrelation when monitoring the mean of processes with and without measurement errors. For processes subjected to a combined effect of autocorrelation and measurement errors, the proposed sampling technique, together with multiple measurement strategy, yields an uniformly better zero-state run-length performance than its two main existing competitors for any autocorrelation level. However, in steady-state mode, it yields the best performance only when the monitoring process is subject to a high level of autocorrelation, for any given level of measurement errors. A real life example is used to illustrate the implementation of the proposed sampling strategy.
为了降低自相关对监测方案的影响，提出了一种新的抽样策略，以形成大小为 的合理子组样本。它要求抽样按以下方式进行：（i）将两个连续样本的观测值合并，以及（ii）在抽样前跳过一些连续观测值。这种技术是混合样本策略的广义版本，结果表明，在监测有无测量误差的过程均值时，它能更好地降低自相关的负面影响。对于受到自相关和测量误差综合影响的过程，所提出的抽样技术与多重测量策略相结合，在任何自相关水平下，其零状态运行长度性能都比现有的两个主要竞争对手始终更好。然而，在稳态模式下，对于任何给定的测量误差水平，只有当监测过程存在高度自相关时，它才会产生最佳性能。通过一个实际例子来说明所提出抽样策略的实施情况。
