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Retrospective analysis for phase I statistical process control and process capability study using revised sample entropy

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Abstract

This study explored a new nonparametric analytical method for identifying heterogeneous segments in time-series data for data-abundant processes. A sample entropy (SampEn) algorithm often used in signal processing and information theory can also be used in a time series or a signal stream, but the original SampEn is only capable of quantifying process variation changes. The proposed algorithm, the adjusted sample entropy (AdSEn), is capable of identifying process mean shifts, variance changes, or mixture of both. A simulation study showed that the proposed method is capable of identifying heterogeneous segments in a time series. Once segments of change points are identified, any existing change-point algorithms can be used to precisely identify exact locations of potential change points. The proposed method is especially applicable for long time series with many change points. Properties of the proposed AdSEn are provided to demonstrate the algorithm’s multi-scale capability. A table of critical values is also provided to help users accurately interpret entropy results.

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Abbreviations

SampEn:

Sample entropy

AdSEn:

Adjusted sample entropy

i.i.d.:

Independent and identically distributed

HDS:

Historical data series

CUSUM:

Cumulative sum

EWMA:

Exponential moving average

ApEn:

Approximate entropy

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Acknowledgements

This work was based on Mr. Zhang’s thesis as partial fulfillment of his MS degree in the Department of Industrial and Manufacturing Systems Engineering at Kansas State University, Manhattan, KS. Mr. Malmir’s support was based on the Biomass Research and Development Initiative Program with Grant No. 2012-10006-20230 from the US Department of Agriculture National Institute of Food and Agriculture. Dr. Kong was supported by the Fundamental Research Funds for the Central Universities projects under Grant Nos. 7214487602 and 72134876 and co-supported by Shaanxi Provincial scientific and technological research projects under Grant No. DF0102130401. He was a research visiting scholar to the IMSE department at Kansas State University.

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Authors and Affiliations

  1. Department of Industrial and Manufacturing Systems Engineering, Kansas State University, Manhattan, 66506, USA

    Shing I. Chang, Zheng Zhang, Siim Koppel & Behnam Malmir

  2. Department of Biological and Agricultural Engineering, Kansas State University, Manhattan, 66506, USA

    Donghai Wang

  3. School of Electromechanical Engineering, Xidian University, Xian, 710071, Shanxi, China

    Xianguang Kong

  4. Department of Statistics, Tamkang University, Tamsui District, New Taipei City, 25137, Taiwan

    Tzong-Ru Tsai

Authors
  1. Shing I. Chang
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  2. Zheng Zhang
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  3. Siim Koppel
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  4. Behnam Malmir
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  5. Xianguang Kong
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  6. Tzong-Ru Tsai
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  7. Donghai Wang
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Correspondence to Shing I. Chang.

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Chang, S.I., Zhang, Z., Koppel, S. et al. Retrospective analysis for phase I statistical process control and process capability study using revised sample entropy. Neural Comput & Applic 31, 7415–7428 (2019). https://doi.org/10.1007/s00521-018-3556-4

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  • DOI: https://doi.org/10.1007/s00521-018-3556-4

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