In this paper we refine and generalize some previous our results on the inaccuracy (error) theory. We define conditions, which characterize different types of functions. Via these functions an indirectly measurable variable Y can be analytically represented. We also present criteria for comparison of the maximal absolute and relative inaccuracies of the indirectly measurable variable Y in the first and in the second order for two experiments. We correct some of our previous conclusions regarding the application of the dimensionless scale for evaluation of the quality of an experiment. Furthermore we give two numerical contra examples.