Fractional replica

With FRFE we differentiale the existence of regular and irregular replicas. A regular fractional replica is obtained from a FUFE matrix by dividing it into a number of parts divisible by two (2, 4, 6, 8, 16, etc.). The obtained replicas are respectively marked by 1/2-replica or half-replica, 1/4-replica, 1/8-replica, etc. Irregular replicas are obtained by taking, for example 3/4 and 5/8 of the FUFE matrix. 

Now consider a fractional replica of type 215 11, which is the 1/2048-replica of a FUFE. It is pointless in this case to write down all aliased/confounded estimates as their number is enormous. As an example, linear effects are aliased/confounded with 105 even interactions. The design matrix of 215 11 is shown in Table 2.96. 

If a fractional replica of type 2k p has been chosen as the core of rotatable design, another expression is used ... 

Equation (2.173) is used for rotatable designs of second and third order when trials are replicated only in null point. In the case of a full factorial experiment or regular fractional replicas, we use ... 

Full factorial experiment and regular fractional replicas Equal replication (2.169) and (2.128)... 

A case of application of fractional replica 27-3 of a full factorial experiment on studying adhesion of thermoplastic polymer and fiber has been analyzed earlier in Example 2.33. Tensile strength of adhesion has been measured as the system response. The experiment included seven factors, with the nature of fiber being a qualitative-categorical factor. The regression coefficient values and method of steepest ascent are shown Table 2.188. 

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