In this paper a method for constructing efficient two-level fractional factorial designs for the analysis of two-step production processes is described. First a design for analyzing the first step of the production process is chosen. The chosen design is then extended to one for analyzing both steps. The design is extended in a such a way that the number of different combinations for the first step is small.
Berkum, van, E. E. M., Habers, E. J., Ven, van de, P., & Wijnen, J. T. M. (2005). Fractional factorial designs for two-step production processes. Journal of Statistical Planning and Inference, 132(1-2), 53-62. https://doi.org/10.1016/j.jspi.2003.10.012