Article: Conditional design of the Shewhart X̄ chart with unknown process parameters based on median run length Journal: European Journal of Industrial Engineering (EJIE) 2023 Vol.17 No.1 pp.90 - 114 Abstract: Numerous researches have been done on the Shewhart X̄ chart based on the average run length (ARL) metric. Since the shape of the run length (RL) distribution changes with the mean shift size, the median run length (MRL) is argued to be a better criterion for evaluating the performance of the Shewhart X̄ chart. Moreover, when the process parameters are unknown, the phase 2 properties of the Shewhart X̄ chart are conditioned on the parameter estimates arising from different practitioners in phase 1. This variability among the estimated process parameters is usually called as the between-practitioners variability. In order to investigate this variability in the conditional MRL values, both the average MRL (AMRL) and the standard deviation of MRL (SDMRL) will be used together in our article. The performance analyses of the MRL-based Shewhart X̄ chart are provided. To prevent too many lower in-control MRL values than the desired one, an appropriate bootstrap approach is adopted to adjust the control limits, and to further balance the in- and out-of-control MRL values of the Shewhart X̄ chart. [Submitted: 26 September 2018; Accepted: 15 January 2022] Inderscience Publishers - linking academia, business and industry through research

Title: Conditional design of the Shewhart X̄ chart with unknown process parameters based on median run length

Authors: XueLong Hu; Philippe Castagliola; AnAn Tang; XiaoJian Zhou

Addresses: School of Management, Nanjing University of Posts and Telecommunications, Nanjing, China ' Université de Nantes, LS2N UMR CNRS, 6004, Nantes, France ' School of Management, Nanjing University of Posts and Telecommunications, Nanjing, China ' School of Management, Nanjing University of Posts and Telecommunications, Nanjing, China

Abstract: Numerous researches have been done on the Shewhart X̄ chart based on the average run length (ARL) metric. Since the shape of the run length (RL) distribution changes with the mean shift size, the median run length (MRL) is argued to be a better criterion for evaluating the performance of the Shewhart X̄ chart. Moreover, when the process parameters are unknown, the phase 2 properties of the Shewhart X̄ chart are conditioned on the parameter estimates arising from different practitioners in phase 1. This variability among the estimated process parameters is usually called as the between-practitioners variability. In order to investigate this variability in the conditional MRL values, both the average MRL (AMRL) and the standard deviation of MRL (SDMRL) will be used together in our article. The performance analyses of the MRL-based Shewhart X̄ chart are provided. To prevent too many lower in-control MRL values than the desired one, an appropriate bootstrap approach is adopted to adjust the control limits, and to further balance the in- and out-of-control MRL values of the Shewhart X̄ chart. [Submitted: 26 September 2018; Accepted: 15 January 2022]

Keywords: Shewhart X̄ chart; median run length; estimated parameters; average median run length; Standard deviation of median run length.

DOI: 10.1504/EJIE.2023.127753

European Journal of Industrial Engineering, 2023 Vol.17 No.1, pp.90 - 114

Accepted: 15 Jan 2022
Published online: 15 Dec 2022 *

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Title: Conditional design of the Shewhart X̄ chart with unknown process parameters based on median run length

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