diff --git a/smt/surrogate_models/tests/test_krg_het_noise.py b/smt/surrogate_models/tests/test_krg_het_noise.py
deleted file mode 100644
index cf1190549..000000000
--- a/smt/surrogate_models/tests/test_krg_het_noise.py
+++ /dev/null
@@ -1,42 +0,0 @@
-"""
-Author: Andres Lopez-Lopera <<andres.lopez_lopera@onera.fr>>
-
-This package is distributed under New BSD license.
-"""
-
-import unittest
-import numpy as np
-
-from smt.surrogate_models import KRG
-from smt.utils.sm_test_case import SMTestCase
-
-
-class Test(SMTestCase):
-    def test_predict_output(self):
-        xt = np.array([0.0, 1.0, 2.0, 3.0, 4.0])
-        yt = np.array([0.0, 1.0, 1.5, 1.1, 1.0])
-
-        # Adding noisy repetitions
-        np.random.seed(6)
-        yt_std_rand = np.std(yt) * np.random.uniform(size=yt.shape)
-        xt_full = np.array(3 * xt.tolist())
-        yt_full = np.concatenate((yt, yt + 0.2 * yt_std_rand, yt - 0.2 * yt_std_rand))
-
-        sm = KRG(
-            theta0=[1.0],
-            eval_noise=True,
-            use_het_noise=True,
-            n_start=1,
-            hyper_opt="Cobyla",
-        )
-        sm.set_training_values(xt_full, yt_full)
-        sm.train()
-
-        yt = yt.reshape(-1, 1)
-        y = sm.predict_values(xt)
-        t_error = np.linalg.norm(y - yt) / np.linalg.norm(yt)
-        self.assert_error(t_error, 0.0, 1e-2)
-
-
-if __name__ == "__main__":
-    unittest.main()
diff --git a/smt/surrogate_models/tests/test_krg_noise.py b/smt/surrogate_models/tests/test_krg_noise.py
new file mode 100644
index 000000000..bd0ea2ace
--- /dev/null
+++ b/smt/surrogate_models/tests/test_krg_noise.py
@@ -0,0 +1,84 @@
+"""
+Author: Andres Lopez-Lopera <<andres.lopez_lopera@onera.fr>>
+
+This package is distributed under New BSD license.
+"""
+
+import unittest
+import numpy as np
+
+from smt.surrogate_models import KRG
+from smt.utils.sm_test_case import SMTestCase
+
+
+class Test(SMTestCase):
+    def test_predict_output(self):
+        xt = np.array([0.0, 1.0, 2.0, 3.0, 4.0])
+        yt = np.array([0.0, 1.0, 1.5, 1.1, 1.0])
+
+        # Adding noisy repetitions
+        np.random.seed(6)
+        yt_std_rand = np.std(yt) * np.random.uniform(size=yt.shape)
+        xt_full = np.array(3 * xt.tolist())
+        yt_full = np.concatenate((yt, yt + 0.2 * yt_std_rand, yt - 0.2 * yt_std_rand))
+
+        sm = KRG(
+            theta0=[1.0],
+            eval_noise=True,
+            use_het_noise=True,
+            n_start=1,
+            hyper_opt="Cobyla",
+        )
+        sm.set_training_values(xt_full, yt_full)
+        sm.train()
+
+        yt = yt.reshape(-1, 1)
+        y = sm.predict_values(xt)
+        t_error = np.linalg.norm(y - yt) / np.linalg.norm(yt)
+        self.assert_error(t_error, 0.0, 1e-2)
+
+    def test_predict_variance(self):
+        # defining the training data
+        xt = np.array([0.0, 1.0, 2.0, 2.5, 4.0])
+        yt = np.array([0.0, 1.0, 1.5, 1.1, 1.0])
+
+        # defining the models
+        sm_noise_free = KRG()  # noise-free Kriging model
+        sm_noise_fixed = KRG(
+            noise0=[1e-1], print_global=False
+        )  # noisy Kriging model with fixed variance
+        sm_noise_estim = KRG(
+            noise0=[1e-1],
+            eval_noise=True,
+            noise_bounds=[1e-2, 1000.0],
+            print_global=False,
+        )  # noisy Kriging model with estimated variance
+
+        # training the models
+        sm_noise_free.set_training_values(xt, yt)
+        sm_noise_free.train()
+
+        sm_noise_fixed.set_training_values(xt, yt)
+        sm_noise_fixed.train()
+
+        sm_noise_estim.set_training_values(xt, yt)
+        sm_noise_estim.train()
+
+        # predictions at training points
+        x = xt
+
+        # error message in case if test case got failed
+
+        # the Variance (interpolation case without noise) must be =/ 0
+        var_noise_free = sm_noise_free.predict_variances(x)  # predictive variance
+        self.assert_error(np.linalg.norm(var_noise_free), 0.0, 1e-5)
+
+        # the Variance (regression case with noise) must be =/ 0
+        var_noise_fixed = sm_noise_fixed.predict_variances(x)  # predictive variance
+        self.assert_error(np.linalg.norm(var_noise_fixed), 0.04768, 1e-5)
+        var_noise_estim = sm_noise_estim.predict_variances(x)  # predictive variance
+        self.assert_error(np.linalg.norm(var_noise_estim), 0.01135, 1e-5)
+
+
+if __name__ == "__main__":
+    unittest.main()