Advertisement

Journal of Statistical Theory and Practice

, Volume 6, Issue 3, pp 580–589 | Cite as

Minimum Cost Linear Trend Free Fractional Factorial Designs

Article

Abstract

Many fractional factorial experiments, especially those of exploratory type, are conducted sequentially in a specific run order. These experiments must be sequenced such that main effects and/or two-factor interactions are orthogonal (i.e., resistant) to the time trend or to any uncontrollable factor aliased with this trend. They must also be sequenced such that factors with expensive or difficult-to-vary levels are minimally varied during experimentation. This article employs the main effects-interactions assignment technique of Cheng and Jacroux (1988) and constructs a catalogue of minimum cost linear trend free regular 2n-(n-k) fractional factorial designs of resolution at least 3. The construction is based on tabulating the complete 2k factorial experiment such that main effects and interactions are in increasing number of level changes from 1 up to (2k - 1), then selecting subtables involving the first n nonmain effects and assigning them to new two-level factors, where (2k-1 - (k - 1) = n = 2k - 1 - k) and k > 2. The paper provides for each linear trend free 2n-(n-k) fraction: (1) the defining relation (i.e., the alias structure), (2) the k independent generators needed for the generalized fold-over run sequencing scheme, (3) the two-factor interactions (if any) that are linear trend free and (4) the total number of factor level changes (i.e., the experimental cost).

62F15 

Keywords

Experimental cost Generalized fold-over scheme Main effects-interactions assignment Minimum factor level changes Sequential fractional factorial experimentation Time trend free run orders 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Cheng, C. S., and M. Jacroux. 1988. The construction of trend-free run orders of two-level factorial designs. J. Am. Stat. Assoc., 83, 1152–1158.MathSciNetCrossRefGoogle Scholar
  2. Cheng, C. S., R. J. Martin, and B. Tang. 1998. Two-level factorial designs with extreme number of level changes. Ann. Stat., 26(4), 1522–1539.MathSciNetCrossRefGoogle Scholar
  3. Correa, A. A., P. Grima, and Tort-Martorell. 2009. Experimentation order with good properties for 2k factorial designs. J. App. Stat., 36(7), 743–754.CrossRefGoogle Scholar
  4. Coster, D. C., and C. S. Cheng. 1988. Minimum cost trend-free run orders of fractional factorial designs. Ann. Stat., 16, 1188–1205.MathSciNetCrossRefGoogle Scholar
  5. Cui, X., and P. W. John. 1998. Time trend free run orders with minimum level changes. Commun. Stat. Theory Methods, 27, 55–68.MathSciNetCrossRefGoogle Scholar
  6. Draper, N. R., and D. M. Stoneman. 1968. Factor level changes and linear trends in eight-run twolevel factorial designs. Technometrics, 10, 301–311.MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2012

Authors and Affiliations

  1. 1.Mathematics DepartmentUniversity of JordanAmmanJordan

Personalised recommendations