A Synthetic Variable Parameter X¯bar Control Charts to Detect Small and Moderate Shifts

Authors

  • Saeed Heydari Department of Statistics, Persian Gulf University, Bushehr, Iran
  • Mahmoud Afshari Department of Statistics, Persian Gulf University, Bushehr, Iran
  • Saeed Tahmasebi Department of Statistics, Persian Gulf University, Bushehr, Iran
  • Ali Akbar Heydari Department of Statistics, University of Tabriz, Tabriz, Iran

Keywords:

Control charts, Markov chain, synthetic control chart, VP control chart

Abstract

Due to the technological advances, the use of control charts is more important than ever. The 
variable parameters (VP) control charts are based on the varying all equation   chart parameters, sample size  equation, sampling interval equation and the  equation   used to determine the action limits. In this paper, we introduce the synthetic-VP equation  chart for monitoring changes in the process mean especially moderate and small shifts. The optimal charting parameters of the proposed chart are obtained using the Markov chain approach. An example is also presented to show the performance of the proposed chart against other charts.



References

Costa AFB. X¯ charts with variable parameters. J Qual Technol. 1999a; 31: 408-416.

Costa AFB. Joint X¯ and R charts with variable sample sizes and sampling intervals. J. Qual. Technol.

b; 31: 387-397.

Costa AFB. The AATS for the X¯ chart with variable parameters. J Qual Technol. 1999c; 31: 455-458.

Davis RB, Woodall WH. Evaluating and improving the synthetic control chart. J Qual Technol. 2002;

: 200-208.

Khoo MBC, Lee HC, Wu Z, Chen CH, Castagliola P. A synthetic double sampling control chart for

the process mean. IIE Trans. 2011; 43: 23-38.

Khoo MBC, Wong VH, Wu Z, Castagliola P. Optimal design of the synthetic chart for the process

mean based on median run length. IIE Trans. 2012; 44: 765-779.

Shewhart WA. Economic Control of Quality of Manufactured Product.1931.

Wan Q, Zhu M, Liu Y. Monitoring the process mean using a synthetic X¯ control chart with two

sampling intervals. J Intell Fuzzy Syst. 2020; 38(4): 4191-4203.

Wu Z, Spedding TA. A synthetic control chart for detecting small shifts in the process mean. J Qual

Technol. 2000; 32: 32-38.

Wu Z, Ou Y, Castagliola P, Khoo MBC. A combined synthetic & X¯ chart for monitoring the process

mean. Int J Prod Res. 2010; 48: 7423-7436.

Yeong WC, Lim SL, Khoo MBC, Castagliola P. Monitoring the coefficient of variation using a variable parameters chart. Qual Eng. 2018; 30(2): 212-235.

Zhou W, Liu N, Zheng Z. A synthetic control chart for monitoring the small shifts in a process mean

based on an attribute inspection. Commun Stat Theor M. 2020; 49(9): 2189-2204.

Zhang Y, Castagliola P, Wu Z, Khoo MBC. The synthetic X- chart with estimated parameters. IIE

Trans. 2011; 43: 676-687.

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Published

2025-06-24

How to Cite

Heydari, S. ., Afshari , M. ., Tahmasebi, S. ., & Akbar Heydari, A. . (2025). A Synthetic Variable Parameter X¯bar Control Charts to Detect Small and Moderate Shifts. Thailand Statistician, 23(3), 512–522. retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/259923

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