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Neural Computing and Applications

, Volume 31, Issue 11, pp 7415–7428 | Cite as

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

  • Shing I. ChangEmail author
  • Zheng Zhang
  • Siim Koppel
  • Behnam Malmir
  • Xianguang Kong
  • Tzong-Ru Tsai
  • Donghai Wang
Original Article

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.

Keywords

Sample entropy Change points Process capability analysis Statistical process control 

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

Notes

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.

Compliance with ethical standards

Conflict of interest

The authors have no conflict of interest to declare.

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Copyright information

© The Natural Computing Applications Forum 2018

Authors and Affiliations

  • Shing I. Chang
    • 1
    Email author
  • Zheng Zhang
    • 1
  • Siim Koppel
    • 1
  • Behnam Malmir
    • 1
  • Xianguang Kong
    • 3
  • Tzong-Ru Tsai
    • 4
  • Donghai Wang
    • 2
  1. 1.Department of Industrial and Manufacturing Systems EngineeringKansas State UniversityManhattanUSA
  2. 2.Department of Biological and Agricultural EngineeringKansas State UniversityManhattanUSA
  3. 3.School of Electromechanical EngineeringXidian UniversityXianChina
  4. 4.Department of StatisticsTamkang UniversityTamsui District, New Taipei CityTaiwan

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