Experiments play an important role in understanding and improving a given system, by manipulating the input variables systematically. Generally, experiments can be classified based on various factors like adaptability, the degree of control on the environment, the destination of its end product/service, etc. In this work, we have chosen the experimental problem proposed in Sudarsanam. et.al.(2018), which considers online experimentation with a finite scope for single factor two-level case. The theoretical results of the optimal number of replicates for such an experiment were discussed in a section in Sudarsanam. et.al. (2019), which dealt with this idea for multi-factor experiments. In this study, we explore the idiosyncrasies of problems that come with different aliasing patterns owing to fractioning of full factorials. In these lines, we propose the theoretical results of the optimal number of replicates for a two-level fractional factorial design with normal distribution assumptions on the experimental responses. These results are then validated by hierarchical probability model (HPM) simulation, which also aids in capturing different scenarios which are not examined by the theoretical results. We extend the above model to a case where the distribution of the response variable is considered to be discrete. Here, three discrete distributions are analyzed, namely the Binomial, Poisson, and Hypergeometric, which cover experimental responses that are either binary or counting variables. In both continuous and discrete cases, the results show that the optimal sample size is dependent on three important parameters which include, signal to noise ratio, size of the finite set, and the number of factors considered. Thus, the final goal of this work is to understand the effect of varying these parameters on the optimal sample size, through sensitivity analysis. This analysis assists in providing recommendations to the practitioners, that should be considered while choosing the parameter values for their setting.