Flexibility analysis is of prime importance in chemical process systems, since it permits the creation of chemical processes, which can satisfy all design specifications in spite of changes in internal and externalfactors during the operation stage. The modem foundations of flexibility analysis were developed in the 1980s by Grossman and coworkers. They formulated solution approaches for the main problems of flexibility analysis (feasibility test), flexibility index, and the two-stage optimization problem. All the formulations are based on the supposition that during the operation stage there are enough experimental data to. accurately determine uncertain parameter values, but in practice, these assumptions are not likely to be met. This article discusses extensions of the feasibility test and the two-stage optimization problem (TSOP), which take into account the possibility of accurately estimating some of the uncertain parameters while estimating with less accuracy the remaining uncertain parameters. To solve the TSOP, the split and bound approach was developed based on a partitioning of the uncertainty region and estimation of bounds on the performance objective function. Three computational experiments show the importance of taking into account the possibility (or lack thereof) of obtaining values of greater accuracy for uncertain parameters at the operation stage.