Plackett-Burman Experimental Design Algorithm

Plackett-Burman designs are two level fractional designs, i.e. each factor or uncertainty variable has a low and a high value ( or a -1 and a +1 value).

The algorithm uses a generator row of plus and minus signs (the plus sign representing a high value and the minus sign a low value).

The first set of variable values is taken from the generator row to create the first simulation deck.
The second set of variable values is taken from a new row that is created by taking the first generator row and moving each element of the row to the right one position.The last element becomes the first element of the new row. 

The third set of values is taken from a row generated from the second row in the same manner, i.e. moving elements one position to the right.
Subsequent rows are produced similarly until k rows have been created. The final k+1th row is a row of minus signs only.

Some examples of generator rows are shown below...

11 variables + + - + + + - - - + -
19 variables + + - - + + + + - + - + - - - - + + -
23 variables + + + + + - + - + + - - + + - - + - + - - - -

An example Plackett-Burman design for 11 uncertainty variables producing 12 simulation runs is shown below....

+ - + - - - + + + - +
+ + - + - - - + + + -
- + + - + - - - + + +
+ - + + - + - - - + +
+ + - + + - + - - - +
+ + + - + + - + - - -
- + + + - + + - + - -
- - + + + - + + - + -
- - - + + + - + + - +
+ - - - + + + - + + -
- + - - - + + + - + +
- - - - - - - - - - -

Although Plackett-Burman is a two level design with only low and high values, in Rezen we add one more row consisting of the middle or zero values for each uncertainty variable. This is so that the ensemble of simulation runs outputs additional data for a central base case run so that a second order proxy equation can take into account any curvature.

Example table showing 5 uncertainty variables with -1,0,+1 values for each variable

rezen pb5_variablelist

Example table showing 11 Plackett-Burman generated simulation decks with their associated uncertainty variable values

rezen pb5uncertaintyvariablevalues


Example table showing 11 Plackett-Burman generated simulation decks with their associated uncertainty variable indices

 

rezen pb5uncertaintyvariableindices