Advantages/disadvantages of fractional factorial design vs completely randomized design I'm new to the design of experiments (DoE) and will be running a screening experiment to estimate the effect of a large number of binary independent variables (approximately 10) on a single continuous dependent variable. It will not be feasible to run all $2^{10}$ factorial experiments, so I have been reading about DoE to understand what the best strategy would be. 
My first intuition was to do a completely randomized design. If I had a budget of $2^5$ experiments, for each experiment I would randomly select the low or high level for each factor with probability 0.5, and repeat this procedure $2^5$ times. On the other hand it seems most common in the DoE literature to use a $2^{10 - 5}$ fractional factorial design, where I would choose 5 independent variables, run the full factorial design for those 5 variables and alias each of the other 5 variables to some combinations of the chosen 5. 
I've been having a hard time finding any discussion online of the relative advantages/disadvantages of these two approaches. I'd love if any DoE experts could weigh in. 
 A: What you propose is to randomize the choice of treatments. That is not a completely randomized design (CRD), a CRD is about randomizing the allocation of experimental units to the treatments. 
Good books like Casella's Statistical Design make an important distinction between the Treatment design and the experimental design. Good experiments need both. To cite:

The title of this book, “Statistical Design”, was chosen purposefully.
  Note that the title of this book is not “Experimental Design”. The
  reason for this is that there are two pieces to a design, which we
  separate into Treatment Design and Experiment Design. A Statistical
  Design contains both of these pieces. 

Your fractional factorial design is the Treatment design. Then, in addition, you need an experimental design. That might be an CRD, or it might be a blocked design, or a split plot, or ... 
In your proposal you are mixing those two concepts. Randomization is important in experimental design, but not in treatment design. Se also the good comment by @Dave2e.
