Experimentation order with good properties for 2kfactorial designs

Correa, Alexander A.; Cintas, Pere Grima; Tort‐Martorell, Xavier

doi:10.1080/02664760802499337

Cited by 29 publications

(15 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…These algorithms are due to Correa et al (2009), Cui and John (1998), Cheng and Jacroux (1988), and Coster and Cheng (1988), referred to here as algorithms I, II, III (a and b), and IV, respectively. The methods of construction of these four algorithms are different, where some use the generalized foldover scheme and some use the interactionsmain effects assignment while others do not use either.…”

Section: Introductionmentioning

confidence: 99%

Three Categories of Minimum Cost Systematic Full 2ⁿFactorial Designs

Hilow

2014

Journal of Statistical Theory and Practice

View full text Add to dashboard Cite

Full 2 n factorial experiments are often conducted sequentially run after run. A full 2 n factorial experiment has a total of 2 n ! permutations among its 2 n runs but not all of these 2 n ! permutations produce runs sequences with good statistical properties. In fact, the standard runs order is not economic (requiring a large number of factor level changes between runs), and does not produce time-trend-resistant main effects. Four main algorithms exist for sequencing runs of the full 2 n factorial experiment such that: (1) main effects and/or two-factor interactions are orthogonal to the linear/quadratic time trend and/or (2) the number of factor level changes between runs (i.e., cost) is minimal = (2 n -1) or minimum. This article proposes, through using the generalized foldover scheme and the interactions-main effects assignment, three categories of systematic full 2 n factorial designs where main effects and/or two-factor interactions are linear/quadratic trend free and where the number of factor level changes is minimal (i.e., (2 n -1)) or less than that of existing algorithms. These three categories are called (i) minimal-cost full 2 n factorial designs, (ii) minimum-cost linear-trend-free full 2 n factorial designs, and (iii) minimum-cost linear and quadratic-trend-free full 2 n factorial designs. A comparison with existing systematic full 2 n factorial designs reveals that the proposed systematic 2 n designs compete well regarding minimization of the number of factor level changes (i.e., cost) or regarding protection of main effects and/or two-factor interactions against the linear/quadratic time trend.

show abstract

Section: Introductionmentioning

confidence: 99%

Three Categories of Minimum Cost Systematic Full 2ⁿFactorial Designs

Hilow

2014

Journal of Statistical Theory and Practice

View full text Add to dashboard Cite

show abstract

“…cost) is 120 calculated by summing the entries of the third row in the bottom of Table 1 designs can be obtained from this largest minimum cost 2 15-(15-4) design by successively deleting some of its last columns to preserve minimality of factor level changes, where deletion of the last column (i.e. factor O) produces a minimum cost 2 14-(14- 4) design and deletion of the last two columns (i.e. factors N and O) produces a minimum cost 2 13-(13-4) design, until the deletion of the last 7 columns which produces the smallest minimum cost 2 8-(8-4) design, where the 4 in- due to [7].…”

Section: Open Access Ojsmentioning

confidence: 99%

“…designs that can be constructed from the full 2 4 experiment by the interactions-main effects assignment, where each design of each category has its own: 1) run sequence in minimum number of factor level changes, 2) defining relation (i.e. resolution) and 3) level in protection of main effects against the linear/quadratic time trend.…”

Section: Open Access Ojsmentioning

confidence: 99%

“…designs that can be constructed from the complete 2 4 factorial experiment by the interactions-main effects assignment for either the protection of main effects against the linear/quadratic time trend and/or for minimizing the number of factor level changes (i.e. cost) between the…”

Section: Characterization Of Six Categories Of 16-run Systematic 2 N-mentioning

confidence: 99%

“…For systematic complete 2 n factorial experiments, there are four main algorithms for sequencing their 2 n runs to overcome either of the above mentioned two problems. These algorithms are due to [1][2][3][4]. [5] has conducted a comparison among these algorithms and documented their differences according to three criteria: 1) which algorithm produces run orders in less number of factor level changes, 2) which algorithm produces run orders with more linear/quadratic time trend free main effects and 3) which run order of an algorithm can be generated by another algorithm using either the generalized foldover scheme or the interactions-main effects assignment.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Characterization of Six Categories of Systematic 2n－(n－k) Fractional Factorial Designs

Hilow¹

2014

OJS

View full text Add to dashboard Cite

Six categories of systematic designs. This paper characterizes these six categories and documents their differences with regard to either time trend resistance of factor effects and/or the number of factor level changes. The paper introduces the last category of systematic the defining relation or its alias structure and 3) the k independent generators needed for sequencing the ( ) 2 n n k − − runs by the generalized foldover scheme. A comparison among these six categories of designs reveals that when the polynomial degree of the time trend increases from linear into quadratic and/or when the design's resolution increases from III to IV, the number of factor level changes between the ( ) 2 n n k − − runs increases. Also as the number of factors (i.e. n) increases, the design's resolution decreases.

show abstract