2 5 1 Fractional Factorial Design

For an n 3n design d φ d 13 12 n 29 27 n 29 27 n n i 1 2 29 i ai d.

2 5 1 fractional factorial design. This is a resolution v design and does not confound main effects and two order interactions but does confound two order interactions with third order interactions. There are very useful summaries of two level fractional factorial designs for up to 11 factors originally published in the book statistics for experimenters by g e p. The top part of figure 3 1 shows the layout of this two by two design which forms the square x space on the left. The equation i bcde is called the defining relation of the 2 5 1 design.

Rather than the 32 runs that would be required for the full 2 5 factorial experiment this experiment requires only eight runs. Useful fractional factorial designs for up to 10 factors are summarized here. A 1 2 fraction can be generated from any interaction but using the highest order interaction is the standard. 2020 with results fractional factorial study design example with results disclaimer.

For example a 2 5 2 design is 1 4 of a two level five factor factorial design. The following information is fictional and is only intended for the purpose of illustrating key concepts for results data entry in the protocol registration and results system prs. There are three generators since this is a 1 8 2 3 fraction in general a 2 k p fractional factorial needs p generators which define the settings for p additional factor columns to be added to the 2 k p full factorial design columns see the following detailed description for the 2 8 3 design. Hunter new york john wiley sons 1978 and also given in the book design and analysis of experiments 5th edition by.

A full factorial design would require 2 5 32 runs with no replications. This design is called a 25 1 fractional factorial design. The 2 5 1 design has only 15 degrees of freedom for estimating factorial effects it cannot estimate all 31 factorial effects among the factors b c d e q. The design is said to have resolution iv because the defining relation consists of the word bcde which has length 4.

A design with p such generators is a 1 l p l p fraction of the full factorial design. Thus designs permuted from a minimum aberration. Uniform fractional factorial designs 895 theorem 2 2. This is too many runs for operations to be willing to handle.

A fractional factorial design uses a subset of a full factorial design so some of the main effects and 2 way interactions are confounded and cannot be separated. Fractional factorial designs are a good choice when resources are limited or the number of factors in the design is large because they use fewer runs than the full factorial designs. Fractional factorial study design example 1 of 47. Two level factorial versus one factor at a time ofat.

You decide to go with 16 runs and use a 2 5 1 fractional factorial. Theorem 2 2 implies that the average centered l2 discrepancy and the mini mum aberration criterion are approximately equivalent as 2 29 i decreases geo metrically when i increases. Aliasing of the effects is a price one must pay for choosing a smaller design.