Complete factorial experiments
A full factorial experiment uses the same number of replicates for every combination of levels for the factors. The number of runs required increases exponentially as the number of factors increases and soon becomes prohibitively expensive even when the factors only have two levels and a single replicate is used. The table below shows the minimum number of runs for different numbers of factors.
Number of factors | ||||||||
---|---|---|---|---|---|---|---|---|
Number of factors | 2 | 3 | 4 | 5 | 6 | 7 | ... | k |
Number of runs | 4 | 8 | 16 | 32 | 64 | 128 | 2k |
Screening experiments may assess ten or more factors, so a different experimental design is needed to keep the number of runs (and hence the cost) down.
Hardness of car paint
The initial part of this study investigates which of 15 additives (A - O) for a car paint has the greatest affect on the hardness of the paint.
A complete factorial experiment with all combinations of the factor levels (absent or present) would require 215 = 32,768 experimental units, even without replication. This is clearly impractical.