Monitoring the log-normal process using bootstrap X̄-R control charts

Lee-Ing Tong*, Chao Ching Hung, Kai Wei Su, Yu Chiun Wang

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The control chart is one of the most frequently utilized tools of statistical process control (SPC) in industry to monitor the process variation. The control limits of Shewhart X̄-R control charts are derived under the assumption that the process data are independently and normally distributed. The false alarm may be increased for X̄-R charts when the process data follow a non-normal distribution (e.g., log-normal distribution). The objective of this study is to utilize the non-parametric bootstrap sampling method and two popular bootstrap confidence intervals (i.e., percentile bootstrap (PB) and bias-corrected and accelerated (BCa)) to construct the X̄-R charts for the log-normal distribution. The sensitivity analysis is conducted to verify the effectiveness of the proposed method. The simulation results indicates that for n = 2 to 5, the control limits of the bootstrap X̄-R charts constructed by PB method performs generally better than that of BCa method and Shewhart X̄-R charts in terms of average run length (ARL) for the log-normal distribution.

Original languageEnglish
Title of host publicationProceedings - 22nd ISSAT International Conference on Reliability and Quality in Design
EditorsHoang Pham
PublisherInternational Society of Science and Applied Technologies
Pages35-39
Number of pages5
ISBN (Electronic)9780991057634
StatePublished - 1 Jan 2016
Event22nd ISSAT International Conference on Reliability and Quality in Design - Los Angeles, United States
Duration: 4 Aug 20166 Aug 2016

Publication series

NameProceedings - 22nd ISSAT International Conference on Reliability and Quality in Design

Conference

Conference22nd ISSAT International Conference on Reliability and Quality in Design
CountryUnited States
CityLos Angeles
Period4/08/166/08/16

Keywords

  • Bootstrap confidence intervals
  • Bootstrap sampling
  • Control charts
  • Log-normal distribution

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  • Cite this

    Tong, L-I., Hung, C. C., Su, K. W., & Wang, Y. C. (2016). Monitoring the log-normal process using bootstrap X̄-R control charts. In H. Pham (Ed.), Proceedings - 22nd ISSAT International Conference on Reliability and Quality in Design (pp. 35-39). (Proceedings - 22nd ISSAT International Conference on Reliability and Quality in Design). International Society of Science and Applied Technologies.