03-09-2016, 11:47 AM
1452353033-Factorialexperimentpraju (1).docx (Size: 25.19 KB / Downloads: 4)
So far we have considered the testing of a number of treatement not necessarily related to each other, in randomized blocks or latin squares or graeco latin squares.in industrial applications frequently we know that several factors may affect the characteristics in which we are interested,and we wish to estimate the effects of each of factors and how the effect of one factor varies over the level of the other factors . for example, the yield of a chemical process may be affected by several factors such as the levels of pressure,temp.,rate of agitation,and proportion of reactants,etc.one might try to test each of the factors sepaeately,holding all other factors constant in a given experiment but with a little thought it might be caler that such an experiment might not given the information required. The logical produre would be to all factors simultaneously,i.e., within the framework of the same experiment. When we do so, we have what is know widely known as a factorial experiment.
The factorial experiment are particularly useful in experimental situation which require the examination of the effects of varying two or more factor in a complete exploration of such a situation it is not sufficient to vary one factor at a time,but that all combination of the different factors levels must be examine in order to elucidate the effect of each factor and the possible ways in which each factor may be modified by the variation of the others. In the analysis of the experimental results,the effect of each factor can be determined with the same accuracy as if only one factor had been varied at a time and the interaction effects between the factors can also be evaluated.
Types of factorial experiment:
22 factorial experiment:
Here we have two factors each at two levels (0,1), say,so that there are 2*2 = 4 treatement combinations in all. Following the notations due to Yates, let the capital letters A and B indicates the names of the two factor under study let the small letters a and b denotes one of the two levels of each of the corresponding factor and this will be called the second level. The first level of A and B generally exprreessed by the absence of the corresponding letter in the treatement combination can be enumerated as follows:
A0b0 or ‘1’ : factors AandB, both at first level.
A1b0 or a : A at second level and B at first level .
A0b1 or b : A at first level and B at second level.
A1b1 or ab : A and B both at second level.