On the conditional performance of the synthetic chart with unknown process parameters using the exceedance probability criterion

PLoS One. 2020 Oct 5;15(10):e0239538. doi: 10.1371/journal.pone.0239538. eCollection 2020.

Abstract

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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Probability
  • Statistics as Topic / methods*

Grants and funding

This research are supported by NSFC No. 71802110, Natural Science Foundation of JiangSu Province No. BK20170894, Humanity and Social Science Youth Foundation of Ministry of Education of China 19YJA630061, Key Research Base of Philosophy and Social Sciences in Jiangsu-Information Industry Integration Innovation and Emergency Management Research Center. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.