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9.1.5 RandomizationThe order of assigning objects or components to the levels of factors and

experimental runs should be randomized as much as possible in order to balance

out the effect of the noise variables on the response variables, to minimizethe bias, and to introduce independence among the observations of the

response variables. This may not be easy or feasible in all experiments.

9.2 Single-Factor ExperimentsIn these experiments, the effect of only one signal factor or input variable on

a response variable is studied.

9.2.1 AnalysisThe following assumptions are made in this design.

1. The single factor is set at a different levels.

2. At each of the levels of the factor, n experiments are conducted;

that is, the number of replications is n.

3. The value of thejth response variable at the ith level of the factor

is denoted byyij, i

1, 2,, a andj

1, 2,, n.4. Theyij for any given level i are independent and follow normal

distribution with a mean

iand variance

2, i 1, 2,, a.Let us consider the following example.