Adaptive Order-of-Addition Experiments via the Quick-Sort Algorithm

References

• Benjamini, Y., and Hochberg, Y. (1995), “Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing,” Journal of the Royal Statistical Society, Series B, 57, 289–300. DOI: 10.1111/j.2517-6161.1995.tb02031.x.
   Web of Science ®Google Scholar
• Bentley, J. L., and McIlroy, M. D. (1993), “Engineering a Sort Function,” Software – Practice and Experience, 23, 1249–1265. DOI: 10.1002/spe.4380231105.
   Web of Science ®Google Scholar
• Chen, J. B., Han, X. X., Lin, D. K. J., Yang, L. Q., and Zhou, Y. D. (2022), “On Ordering Problem: A Statistical Approach,” Statistica Sinica, forthcoming. DOI: 10.5705/ss.202021.0160.
   PubMedGoogle Scholar
• Chen, J. B., Mukerjee, R., and Lin, D. K. J. (2020), “Construction of Optimal Fractional Order-of-Addition Designs via Block Designs,” Statistics Probability Letters, 161, 108728. DOI: 10.1016/j.spl.2020.108728.
   Web of Science ®Google Scholar
• Chen, J. B., Peng, J. Y., and Lin, D. K. J. (2021), “A Statistical Perspective on Non-deterministic Polynomial-Time Hard Ordering Problems: Making Use of Design for Order-of-Addition Experiments,” Computer & Industrial Engineering, 162, 107773. DOI: 10.1016/j.cie.2021.107773.
   Web of Science ®Google Scholar
• Chen, J. B., Zhang, X. R., Liu, M. Q., and Lin, D. K. J. (2021), “Analysis of Replicated Order-of-Addition Experiments,” Statistics and Applications, 19, 453–466.
   Web of Science ®Google Scholar
• Hoare, C. A. R. (1962), “Quick Sort,” The Computer Journal, 5, 10–15. DOI: 10.1093/comjnl/5.1.10.
   Web of Science ®Google Scholar
• Hossain, M. S., Mondal, S., Ali, R. S., and Hasan, M. (2020), “Optimizing Complexity of Quick Sort,” in: Computing Science, Communication and Security. COMS2 2020. Communications in Computer and Information Science, Vol. 1235, eds. N. Chaubey, S. Parikh, and K. Amin, pp. 329–339, Singapore: Springer.
   Google Scholar
• Jiang, X. J., and Ng, D. K. P. (2014), “Sequential Logic Operations with a Molecular Keypad Lock with Four Inputs and Dual Fluorescence Outputs,” Angewandte Chemie International Edition, 53, 10481–10484. DOI: 10.1002/anie.201406002.
   PubMed Web of Science ®Google Scholar
• Kushagra, S., Alejandro López-Ortiz, A., Ian Munro, J., and Aurick Qiao, A. (2014), “Multi-Pivot Quick Sort: Theory and Experiments,” in: Meeting on Algorithm Engineering & Experiments (ALENEX), 47–60, Philadelphia, PA, USA, 2014. AMS.
   Google Scholar
• Leung, J. Y. T. (2004), Handbook of Scheduling: Algorithms, Models and Performance Analysis, London: Chapman and Hall.
   Google Scholar
• Lin, D. K. J., and Peng, J. Y. (2019), “The Order-of-Addition Experiments: A Review and Some New Thoughts,” (with Discussion), Quality Engineering, 31, 49–59. DOI: 10.1080/08982112.2018.1548021.
   Web of Science ®Google Scholar
• Mee, R. W. (2020), “Order of Addition Modeling,” Statistica Sinica, 30, 1543–1559. DOI: 10.5705/ss.202018.0210.
   Web of Science ®Google Scholar
• Pimedo, M. (2016), Scheduling Theory, Algorithms, and Systems (5th ed.), New York: Springer.
   Google Scholar
• Peng, J. Y., Mukerjee, R., and Lin, D. K. J. (2019), “Design of Order-of-Addition Experiments,” Biometrika, 106, 683–694. DOI: 10.1093/biomet/asz025.
   Web of Science ®Google Scholar
• Philippas, T., and Zhang, Y. (2003), “A Simple, Fast Parallel Implementation of Quick Sort and its Performance Evaluation on SUN Enterprise 10000,” in Proceedings of the 11th Euromicro Conference on Parallel, Distributed and Network-Based Processing (PDP), pp. 372–381, IEEE.
   Google Scholar
• Stokes, Z., and Xu, H. Q. (2022), “A Position-based Approach for Design and Analysis of Order-of-Addition Experiments,” Statistica Sinica, forthcoming. DOI: 10.5705/ss.202020.0178.
   Web of Science ®Google Scholar
• Van Nostrand, R. C. (1995), “Design of Experiments where the Order of Addition is Important,” in ASA Proceedings of the Section on Physical and Engineering Sciences, pp. 155–160. Alexandria, Virginia: American Statistical Association.
   Google Scholar
• Yaroslavskiy, V. (2009), “Dual-Pivot Quick Sort Algorithm,” available at http://codeblab.com/wp-content/uploads/2009/09/DualPivotquicksort.pdf.
   Google Scholar
• Voelkel, J. G. (2019), “The Design of Order-of-Addition Experiments,” Journal of Quality Technology, 51, 230–241. DOI: 10.1080/00224065.2019.1569958.
   Web of Science ®Google Scholar
• Voelkel, J. G., and Gallagher, K. P. (2019), “The Design and Analysis of Order-of-Addition Experiments: An Introduction and Case Study,” Quality Engineering, 31, 627–638. DOI: 10.1080/08982112.2019.1578374.
   Web of Science ®Google Scholar
• Winker, P., Chen, J. B., and Lin, D. K. J. (2020), “The Construction of Optimal Design for Order-of-Addition Experiment via Threshold Accepting,” in Contemporary Design of Experiments, Multivariate Analysis and Data mining—In Celebration of Prof. Kai-Tai Fang’s 80th Birthday, pp. 93–109, Springer.
   Google Scholar
• Wang, C. Y., and Mee, R. W. (2022), “Saturated and Supersaturated Order-of-Addition Designs,” Journal of Statistical Planning and Inference, 219, 204–215. DOI: 10.1016/j.jspi.2021.12.006.
   Web of Science ®Google Scholar
• Xiao, Q., and Xu, H. Q. (2021), “A Mapping-based Universal Kriging Model for Order-of-Addition Experiments in Drug Combination Studies,” Computational Statistics & Data Analysis, 157, 107155. DOI: 10.1016/j.csda.2020.107155.
   Web of Science ®Google Scholar
• Yang, J. F., Sun, F. S., and Xu, H. Q. (2021), “A Component-Position Model, Analysis and Design for Order-of-Addition Experiments,” Technometrics, 63, 212–224. DOI: 10.1080/00401706.2020.1764394.
   Web of Science ®Google Scholar
• Zhang, X. R., Liu, M. Q., Lin, D. K. J., and Chen, J. B. (2022), “Analysis of Order-of-Addition Experiments, manuscript.
   Google Scholar
• Zhao, Y. N., Lin, D. K. J., and Liu, M. Q. (2021), “Designs for Order-of-Addition Experiments,” Journal of Applied Statistics, 48, 1475–1495. DOI: 10.1080/02664763.2020.1801607.
   PubMed Web of Science ®Google Scholar
• Zhao, Y. N., Lin, D. K. J., and Liu, M. Q. (2022), “Optimal Designs for Order-of-Addition Experiments,” Computational Statistics & Data Analysis, 165, 107320.
   Web of Science ®Google Scholar