A First Course in Quality Engineering, 2nd Edition

Quality in Production—Process Control II 357

The major problem with a 2

k

design is that when k increases, the number

of trials needed increases exponentially—even for a single replicate of the

experiment� If multiple replications are needed to estimate the experimen-

tal error, the number of trials becomes impractical� For example, if k = 5

and two replicates are needed, the required number of trials is 64, which is

an enormous number considering the time and other resource constraints

in the context of real processes� Therefore, statisticians have devised meth-

ods to eliminate the need for a second replicate to estimate the error� They

have also devised fractional factorial designs, which call for running only

a fraction of the total ...