Randomization has been proposed  for the dilution-series problem with the purpose of producing a continuous random variable; the randomization is performed by selecting a value from the uniform distribution (0, 1]. This paper develops a structural model appropriate to a range of problems involving such randomization as part of the design. The model applies to the dilution series problem and to the bioassay problem, and produces a posterior distribution for the primary parameter and a marginal likelihood for other parameters.
D. A. S. Fraser. R. L. Prentice. "Randomized Models and the Dilution and Bioassay Problems." Ann. Math. Statist. 42 (1) 141 - 146, February, 1971. https://doi.org/10.1214/aoms/1177693501