I have 5 factors (pH, time, current density, agitation speed of agitation, and the concentration of the effluent) and I am trying to find out which are the most important in my response. What is the plan that I should use for this purpose? I am hesitating using definite screening design, 2^(5–1) Half-Fractional Factorial Design, or Plackett-Burman design?
Use of Definitive Screening Design is recommended because it decreases the number of trials you need to perform. In short: your time, cost and effort will be greatly saved. Moreover, it accomodates categorical variables. Very few articles are available explaining this technique.
For details, you can refer to my article, wherein detailed analysis is also discussed.
https://www.researchgate.net/publication/309383755_Multi_Response_Simulation_and_Optimization_of_Gas_Tungsten_Arc_Welding?_sg=8w39AJtEjtblbU7rQQSlgQ1c2iDDWjw5bcHtAp85vp5Y8SdFGRDsNqXcLXDyaQ-MISkH3-GAfBc6AQG8RdCG8tv8R4KC6vlwMoyC_p53.Pm1Tj8DiSFla_c5Y4Kp2_KJfJREE2yzvT7HVn16Nx_C04uw5Ib6vzuDVqfqjxQp8cOAcJgm8irtYQdeV0df7vw
You should definitely use the fractional factional factorial design and especially the 2^(5-1) has due to combinatorial reasons very good properties. With such a design you will also be able to calculate interaction effects besides main factor effects that you will not be able to perform if using a Plackett-Burman design.
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In addition to the Mattias Andersson contribution, that I agree with, you should be aware that the main effect estimates will be confounded with the 4-factor interaction effects and that the 2-factor interactions will be confounded with the effects of the 3-factor interactions (Resolution V design). This is the price to pay for performing just 16 experiments instead of the full factorial 32 experiments. In IMHO, this definitively better than performing a design where no interactions could be estimated at all (Plackett-Burman, for instance).
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