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Economic design of Shewhart control charts for monitoring autocorrelated data with skip sampling strategies

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  • Franco, Bruno Chaves
  • Celano, Giovanni
  • Castagliola, Philippe
  • Costa, Antonio Fernando Branco

Abstract

On-line monitoring of process variability is strategic to achieve high standards of quality and maintain at acceptable levels the number of nonconforming items. Shewhart control charts are the simplest Statistical Process Control (SPC) procedure to achieve this goal. An efficient implementation of a control chart requires the optimal selection of its design parameters. They can be selected according to an economic-statistical objective: an expected total cost per unit of time incurred during production is minimized subject to a statistical constraint limiting the number of false alarms issued by the control chart. This paper investigates the economic-statistical design of Shewhart control charts implementing skip sampling strategies for constructing subgroups and monitoring autocorrelated AR(1) processes. Implementing skip sampling strategies within a rational subgroup reduces the negative effects of autocorrelation on the statistical performance of the Shewhart control chart. A wide benchmark of examples has been generated as a screening experimental design to study the process and cost factors influencing the selection of the sampling strategy. Regression models have been fitted to the results to help practitioners in the selection of the most convenient sampling strategy. Finally, a sensitivity analysis has been performed to evaluate how the parameters misspecification biases the evaluation of the optimal cost per unit of time.

Suggested Citation

  • Franco, Bruno Chaves & Celano, Giovanni & Castagliola, Philippe & Costa, Antonio Fernando Branco, 2014. "Economic design of Shewhart control charts for monitoring autocorrelated data with skip sampling strategies," International Journal of Production Economics, Elsevier, vol. 151(C), pages 121-130.
    • Handle: RePEc:eee:proeco:v:151:y:2014:i:c:p:121-130
    DOI: 10.1016/j.ijpe.2014.02.008
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    References listed on IDEAS

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    1. Celano, Giovanni & De Magalhães, Maysa S. & Costa, Antonio F.B. & Fichera, Sergio, 2011. "A stochastic shift model for economically designed charts constrained by the process stage configuration," International Journal of Production Economics, Elsevier, vol. 132(2), pages 315-325, August.
    2. Chen, Yan-Kwang & Hsieh, Kun-Lin & Chang, Cheng-Chang, 2007. "Economic design of the VSSI control charts for correlated data," International Journal of Production Economics, Elsevier, vol. 107(2), pages 528-539, June.
    3. Simpson, James R. & Keats, J. Bert, 1995. "Sensitivity study of the CUSUM control chart with an economic model," International Journal of Production Economics, Elsevier, vol. 40(1), pages 1-19, June.
    4. Costa, Antonio Fernando Branco & Machado, Marcela Aparecida Guerreiro, 2011. "Variable parameter and double sampling charts in the presence of correlation: The Markov chain approach," International Journal of Production Economics, Elsevier, vol. 130(2), pages 224-229, April.
    5. Torng, Chau-Chen & Lee, Pei-Hsi & Liao, Nai-Yi, 2009. "An economic-statistical design of double sampling control chart," International Journal of Production Economics, Elsevier, vol. 120(2), pages 495-500, August.
    6. Giovanni Celano, 2009. "Robust design of adaptive control charts for manual manufacturing/inspection workstations," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(2), pages 181-203.
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    Cited by:

    1. Chenglong Li & Amitava Mukherjee & Qin Su & Min Xie, 2016. "Optimal design of a distribution-free quality control scheme for cost-efficient monitoring of unknown location," International Journal of Production Research, Taylor & Francis Journals, vol. 54(24), pages 7259-7273, December.
    2. Naderkhani, Farnoosh & Makis, Viliam, 2016. "Economic design of multivariate Bayesian control chart with two sampling intervals," International Journal of Production Economics, Elsevier, vol. 174(C), pages 29-42.
    3. Lim, S.L. & Khoo, Michael B.C. & Teoh, W.L. & Xie, M., 2015. "Optimal designs of the variable sample size and sampling interval X¯ chart when process parameters are estimated," International Journal of Production Economics, Elsevier, vol. 166(C), pages 20-35.
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    5. Tomohiro, Ryosuke & Arizono, Ikuo & Takemoto, Yasuhiko, 2020. "Economic design of double sampling Cpm control chart for monitoring process capability," International Journal of Production Economics, Elsevier, vol. 221(C).
    6. Roberto Campos Leoni & Marcela Aparecida Guerreiro Machado & Antonio Fernando Branco Costa, 2016. "The T -super-2 chart with mixed samples to control bivariate autocorrelated processes," International Journal of Production Research, Taylor & Francis Journals, vol. 54(11), pages 3294-3310, June.
    7. Xiao, Xiao & Jiang, Wei & Luo, Jianwen, 2019. "Combining process and product information for quality improvement," International Journal of Production Economics, Elsevier, vol. 207(C), pages 130-143.
    8. Leoni, Roberto Campos & Costa, Antonio Fernando Branco & Machado, Marcela Aparecida Guerreiro, 2015. "The effect of the autocorrelation on the performance of the T2 chart," European Journal of Operational Research, Elsevier, vol. 247(1), pages 155-165.
    9. Chenglong Li & Qin Su & Min Xie, 2016. "Economic modelling for statistical process control subject to a general quality deterioration," International Journal of Production Research, Taylor & Francis Journals, vol. 54(6), pages 1753-1770, March.

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