School of Management, Nanjing University of Posts and Telecommunications, Nanjing, China.
Institute of High-Quality Development Evaluation, Nanjing University of Posts and Telecommunications, Nanjing, China.
PLoS One. 2020 Oct 5;15(10):e0239538. doi: 10.1371/journal.pone.0239538. eCollection 2020.
Recent researches on the control charts with unknown process parameters have noticed the large variability in the conditional in-control average run length (ARL) performance of control charts, especially when a small number of Phase I samples is used to estimate the process parameters. Some research works have been conducted on the conditional ARL performance of different types of control charts. In this paper, by simulating the empirical distribution of the conditional ARL and especially using the exceedance probability criterion (EPC), we study the conditional ARL performance of the synthetic [Formula: see text] chart. Our results show that a large amount of Phase I samples is needed to obtain a specified EPC of the synthetic chart. For the available number of Phase I samples, the control limits of the synthetic chart are adjusted using the EPC method to improve its conditional in-control performance. It is shown that, for small mean shift sizes, a tradeoff should be made between the conditional in-control and out-of-control performances. For moderate to large shifts, the conditional performance of the synthetic chart using the adjusted control limits is generally satisfied. By comparing the results with the ones using the bootstrap approach, it can also be concluded that the conditional performances of both approaches are comparable. While the method proposed in this paper requires much less computation work than the bootstrap approach.
最近对具有未知过程参数的控制图的研究注意到，控制图的条件在控平均运行长度（ARL）性能具有很大的可变性，特别是当使用少量 Phase I 样本估计过程参数时。已经对不同类型的控制图的条件 ARL 性能进行了一些研究工作。在本文中，通过模拟条件 ARL 的经验分布，特别是使用超越概率准则（EPC），我们研究了综合 [Formula: see text] 图的条件 ARL 性能。我们的结果表明，需要大量的 Phase I 样本才能获得综合图的指定 EPC。对于可用的 Phase I 样本数量，使用 EPC 方法调整综合图的控制限，以提高其在控性能。结果表明，对于小的均值偏移量，应在条件在控和失控性能之间进行权衡。对于中等至较大的偏移量，使用调整后的控制限的综合图的条件性能通常令人满意。通过将结果与使用自举方法的结果进行比较，还可以得出结论，这两种方法的条件性能相当。虽然本文提出的方法所需的计算工作量比自举方法少得多。
