Durbin's rank test is widely used for testing treatment effects in Balanced Incomplete Block Designs (BIBDs) which have wide applications in sensory analysis. This test is failed for BIBDs when ties data occur. An adjusted version of Durbin rank test for this kind of data is given to solve this problem. Chi-square approximation, which is commonly used for this test, is not adequate for small BIBDs. For this case, we investigate permutation approach for adjusted Durbin rank test. Also, in this study the tests used in BIBDs are compared by simulation study for tied data, which have not been discussed in the sensory literature.