Skip to main content
Log in

Mixed two- and eight-level fractional factorial split-plot designs containing clear effects

  • Published:
Acta Mathematicae Applicatae Sinica, English Series Aims and scope Submit manuscript

Abstract

Fractional factorial split-plot (FFSP) designs are useful in practical experiments. When the numbers of levels of the factors are not all equal in an experiment, mixed-level design is selected. This paper investigates the conditions of a resolution III or IV FFSP design with both two-level and eight-level factors to have various clear effects, including two types of main effects and three types of two-factor interaction components.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Addelman S. Orthogonal main-effect plans for asymmetrical factorial experiments. Technometrics, 4: 21–46 (1962)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chen H., Hedayat A.S. 2n-m designs with resolution III and IV containing clear two-factor interactions. Journal of Statistical Planning and Inference, 75: 147–158 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  3. Wu C.F.J., Chen Y. A graph-aided method for planning two-level experiments when certain interactions are important. Technometrics, 34: 162–175 (1992)

    Article  Google Scholar 

  4. Yang J.F., Li P.F., Liu M.Q., Zhang R.C. \({2^{\left( {{n_1} + {n_2}} \right) - \left( {{k_1} + {k_2}} \right)}}\) fractional factorial split-plot designs containing clear effects. Journal of Statistical Planning and Inference, 136(12): 4450–4458 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. Yang J.F., Liu M.Q., Zhang R.C. Some results on fractional factorial split-plot designs with multi-level factors. Communications in Statistics-Theory and Methods, 38: 3623–3633 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Zhao S.L., Chen X.F. Mixed-level fractional factorial split-plot designs containing clear effects. Metrika, 75: 953–962 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  7. Zhao S.L., Chen X.F. Mixed two- and four-level fractional factional split-plot designs with clear effects. Journal of Statistical Planning and Inference, 142(7): 1789–1793 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  8. Zhao S.L., Zhang R.C. 2m4n designs with resolution III or IV containing clear two-factor interaction components. Statical Papers, 49: 441–454 (2008)

    Article  MATH  Google Scholar 

  9. Zhao S.L., Zhang R.C., Liu M.Q. Some results on 4m2n designs with clear two-factor interaction components. Science in China (Series A), 51: 1297–1314 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. Zi X.M., Zhang R.C., Liu M.Q. Bounds on the maximum numbers of clear two-factor interactions for \({2^{\left( {{n_1} + {n_2}} \right) - \left( {{k_1} + {k_2}} \right)}}\) fractional factorial split-plot designs. Science in China (Series A), 49: 1816–1829 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. Zi X.M., Zhang R.C., Liu M.Q. On optimal two-level nonregular factorial split-plot designs. Journal of Complexity, 28: 459–467 (2012)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sheng-li Zhao.

Additional information

Supported by the National Natural Science Foundation of China (Nos. 10901092, 11171165, 11171188), Shandong Provincial Scientific Research Reward Foundation for Excellent Young and Middle-aged Scientists (BS2011SF006) and Program for Scientific Research Innovation Team in Colleges and Universities of Shandong Province.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yuan, Y., Zhao, Sl. Mixed two- and eight-level fractional factorial split-plot designs containing clear effects. Acta Math. Appl. Sin. Engl. Ser. 32, 995–1004 (2016). https://doi.org/10.1007/s10255-016-0620-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10255-016-0620-7

Keywords

2000 MR Subject Classification

Navigation