Adaptive CUSUM Location Control Charts Based on Score Functions: An Application in Semiconductor Wafer Field

Babar Zaman, Muhammad Riaz, Mu’azu Ramat Abujiya, Muhammad Hisyam Lee*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


An adaptive CUSUM (ACUSUM) control chart got special attention against classical CUSUM control chart to detect a shift of different sizes in the process location. Similarly, an ACUSUM based on classical EWMA statistic and score function, denoted as a ACUSUM E control chart, is improved form of classical CUSUM control chart and can identify different sizes of shift. Classical EWMA statistic in ACUSUM E control chart fails to offer clear instruction for parameter values to identify a precise shift as the classical CUSUM statistic does. To address this issue, this study proposed two ACUSUM control charts, symbolized as ACUSUMC(1) and ACUSUMC(2) to further improve detection ability of shift in the process location. Novelty of the proposed control charts is to initially adaptively renew reference parameters values based on classical CUSUM statistic and then to assign a weight on it using score functions. An algorithm is developed in MATLAB using Monte Carlo simulation method to obtain numerical results. Based on numerical results, performance measures such as average run length for a specific shift, extra quadratic loss, relative average run length, and performance comparison index for overall performance are calculated for comparison purpose. Comparison based on visual presentation and numerical results reveals the proposed control charts performed quite effective against some existing control charts. It is worthy to mention, classical CUSUM control chart is special cases of proposed ACUSUMC(1) control charts at specific values of parameter. Finally, proposed control charts are also implemented on real-life data to show practical significance to users and practitioners.

Original languageEnglish
Pages (from-to)3725-3749
Number of pages25
JournalArabian Journal for Science and Engineering
Issue number3
StatePublished - Mar 2022

Bibliographical note

Funding Information:
The authors are grateful to the editor, and anonymous referees for their many valuable comments and suggestions.

Publisher Copyright:
© 2021, King Fahd University of Petroleum & Minerals.


  • Adaptive
  • Monte Carlo simulation
  • Performance measures
  • Score functions

ASJC Scopus subject areas

  • General


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