A sensitivity analysis may reveal surprising insights in multi-criteria decision making (MCDM) studies aimed to select the best alternative among a number of competing alternatives.
By critical, we mean that a criterion with small change (as a percentage) in its weight, may cause a significant change of the final solution.
It is possible criteria with rather small weights of importance (i.e., ones that are not so important in that respect) to be much more critical in a given situation than ones with larger weights.
[1][2] That is, a sensitivity analysis may shed light into issues not anticipated at the beginning of a study.
This, in turn, may dramatically improve the effectiveness of the initial study and assist in the successful implementation of the final solution.