Statistics Toolbox

Full Factorial Designs

Suppose you want to determine whether the variability of a machining process is due to the difference in the lathes that cut the parts or the operators who run the lathes.

If the same operator always runs a given lathe then you cannot tell whether the machine or the operator is the cause of the variation in the output. By allowing every operator to run every lathe you can separate their effects.

This is a factorial approach. fullfact is the function that generates the design. Suppose you have four operators and three machines. What is the factorial design?

• d = fullfact([4 3])
  
  d =
       1     1
       2     1
       3     1
       4     1
       1     2
       2     2
       3     2
       4     2
       1     3
       2     3
       3     3
       4     3
  

Each row of d represents one operator/machine combination. Note that there are 4*3 = 12 rows.

One special subclass of factorial designs is when all the variables take only two values. Suppose you want to quickly determine the sensitivity of a process to high and low values of three variables.

• d2 = ff2n(3)
  
  d2 =
       0     0     0
       0     0     1
       0     1     0
       0     1     1
       1     0     0
       1     0     1
       1     1     0
       1     1     1
  

There are 2³ = 8 combinations to check.

Introduction

Fractional Factorial Designs