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THERE ARE TWO TYPES OF FACTORIAL DESIGNS: FULL FACTORIAL DESIGN AND FRACTIONAL FACTORIAL DESIGN

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THERE ARE TWO TYPES OF FACTORIAL DESIGNS: FULL FACTORIAL DESIGN AND FRACTIONAL FACTORIAL DESIGN

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A factorial design is a type of designed experiment that lets us study the effects that several factors which can have on a response.

When conducting an experiment, varying the levels of all factors at the same time instead of one at a time lets you study the interactions between the factors.
such as determining the variable which would have the strongest influence on the response.

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Fit and Diagnostics for Unusual Observations

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Fit and Diagnostics for Unusual Observations

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- Shows unusual observation that could be outliers.

E.g. Observation 24 from the data is UNUSUAL.

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STEEPER gradient -> MORE SIGNIFICANT the factor is on the response.

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If the factors are numeric, it can be used to PREDICT the results using the equation.

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p-value < alpha value -> factor affect significantly
-> there is interaction between the factors
p-value > alpha value -> factor DOES NOT affect significantly
-> there is NO interaction between the factors

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-replication helps in verifying the results and gives better estimation o fthe experimental variability and the effects of the factors
- more replicates, the more precise will be the model

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- all measurements are usually subjected to variation and uncertainty
- measurements of the same setting are often repeated, and the full set of experiment is replicated
- replication of experiment will help to identify the sources of variation and to better estimate teh true effects of the treatment

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- Factors that cross the red dotted line = factors affect significantly
- Factors that did not cross the red dotted line = factors DOES NOT affect significantly

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1st factor: Group as a cluster
2nd factor: Writing out the variable in each level twice as shown
3rd factor: Writing out the variable in each level 4 times as shown.

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E.g. Current at 11kA, 16 Cycles and Force at 4kN gives the highest strength of 508.

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its a systematic way to place the experimental factor level of total factorial effect in a standard order

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i.e. cube plots,  factorial regression, analysis of variance table,  normal plots,  Pareto chart, residual plots, normal probability plot.

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TO BE USED WHEN WE WANT TO:
- Effectively calculate each factor's influence on the response.
- to calculate how one or more elements may combine to affect the outcome.
- By integrating center points in the design, check for curvature in the response.

A full factorial design is a design in which researchers measure responses at all combinations of the factor levels. which Minitab offers us two types of full factorial designs:

2-level full factorial designs that contain only 2-level factors.

general full factorial designs that contain factors with more than two levels.

The number of runs necessary for a 2-level full factorial design is 2k where k is the number of factors. As the number of factors in a 2-level factorial design increases, the number of runs necessary to do a full factorial design increases quickly.

For example, a 2-level full factorial design with 6 factors requires 64 runs; a design with 9 factors requires 512 runs. A half-fraction, fractional factorial design would require only half of those runs.

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2^3 = 8 runs

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A 2k full factorial design is an experimental design of k factors with each factor having 2 levels.
The design will have a total of 2 k runs.

k= number of factors