Randomization has been proposed [1] 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.