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Performing successful experiments is a crucial topic for scientists. The selection of factors and levels that have significant effects on the outputs is the most hard problem they may face. For a perfect procedure, a small number of runs (trials) are preferred as an initial-stage experiment (ISExp) for gaining prior information about the influence (importance) of the suggested factors and levels. After analysing the ISExp, the following prior information may arise: (i) the number of parameters in the used model is much larger than the expected number of runs and thus more runs need to be added; (ii) some of the ignored or fixed factors may be active and need further investigations; (iii) extending the levels of some active factors is necessary for optimising the outputs; and/or (iv) the impacts of the active factors are not equally important and thus different weights need be assigned to the factors to identify their importance. Therefore, follow-up experiments (FuExps) need to be conducted for adding new active factors, levels, runs, and/or factor-weights to the ISExps. This paper provides novel techniques for designing FuExps to deal with these real-life scenarios for ISExp with a mixture of two-level factors and four-level factors. To clarify the power and efficiency of the proposed techniques, numerical and theoretical justifications are given.

Novel techniques for performing successful follow-up experiments based on prior information from initial-stage experiments