diff --git a/src/test/java/org/opensearch/ad/model/AnomalyDetectorTests.java b/src/test/java/org/opensearch/ad/model/AnomalyDetectorTests.java
index bc634a869..6c7fe98cd 100644
--- a/src/test/java/org/opensearch/ad/model/AnomalyDetectorTests.java
+++ b/src/test/java/org/opensearch/ad/model/AnomalyDetectorTests.java
@@ -338,7 +338,7 @@ public void testInvalidShingleSize() throws Exception {
                     TestHelpers.randomUser(),
                     null,
                     TestHelpers.randomImputationOption(featureList),
-                    randomIntBetween(1, 10000),
+                    randomIntBetween(2, 10000),
                     randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
                     randomIntBetween(1, 1000),
                     null,
@@ -376,7 +376,7 @@ public void testNullDetectorName() throws Exception {
                     TestHelpers.randomUser(),
                     null,
                     TestHelpers.randomImputationOption(featureList),
-                    randomIntBetween(1, 10000),
+                    randomIntBetween(2, 10000),
                     randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
                     randomIntBetween(1, 1000),
                     null,
@@ -414,7 +414,7 @@ public void testBlankDetectorName() throws Exception {
                     TestHelpers.randomUser(),
                     null,
                     TestHelpers.randomImputationOption(featureList),
-                    randomIntBetween(1, 10000),
+                    randomIntBetween(2, 10000),
                     randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
                     randomIntBetween(1, 1000),
                     null,
@@ -452,7 +452,7 @@ public void testNullTimeField() throws Exception {
                     TestHelpers.randomUser(),
                     null,
                     TestHelpers.randomImputationOption(featureList),
-                    randomIntBetween(1, 10000),
+                    randomIntBetween(2, 10000),
                     randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
                     randomIntBetween(1, 1000),
                     null,
@@ -490,7 +490,7 @@ public void testNullIndices() throws Exception {
                     TestHelpers.randomUser(),
                     null,
                     TestHelpers.randomImputationOption(featureList),
-                    randomIntBetween(1, 10000),
+                    randomIntBetween(2, 10000),
                     randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
                     randomIntBetween(1, 1000),
                     null,
@@ -528,7 +528,7 @@ public void testEmptyIndices() throws Exception {
                     TestHelpers.randomUser(),
                     null,
                     TestHelpers.randomImputationOption(featureList),
-                    randomIntBetween(1, 10000),
+                    randomIntBetween(2, 10000),
                     randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
                     randomIntBetween(1, 1000),
                     null,
@@ -566,7 +566,7 @@ public void testNullDetectionInterval() throws Exception {
                     TestHelpers.randomUser(),
                     null,
                     TestHelpers.randomImputationOption(featureList),
-                    randomIntBetween(1, 10000),
+                    randomIntBetween(2, 10000),
                     randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
                     randomIntBetween(1, 1000),
                     null,
@@ -730,7 +730,7 @@ public void testGetShingleSize() throws IOException {
             TestHelpers.randomUser(),
             null,
             TestHelpers.randomImputationOption(featureList),
-            randomIntBetween(1, 10000),
+            randomIntBetween(2, 10000),
             randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
             randomIntBetween(1, 1000),
             null,
@@ -766,7 +766,7 @@ public void testGetShingleSizeReturnsDefaultValue() throws IOException {
             TestHelpers.randomUser(),
             null,
             TestHelpers.randomImputationOption(featureList),
-            randomIntBetween(1, 10000),
+            randomIntBetween(2, 10000),
             seasonalityIntervals,
             randomIntBetween(1, 1000),
             null,
@@ -832,7 +832,7 @@ public void testNullFeatureAttributes() throws IOException {
             TestHelpers.randomUser(),
             null,
             null,
-            randomIntBetween(1, 10000),
+            randomIntBetween(2, 10000),
             randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
             randomIntBetween(1, 1000),
             null,
@@ -866,7 +866,7 @@ public void testValidateResultIndex() throws IOException {
             TestHelpers.randomUser(),
             null,
             null,
-            randomIntBetween(1, 10000),
+            randomIntBetween(2, 10000),
             randomIntBetween(1, TimeSeriesSettings.MAX_SHINGLE_SIZE * TimeSeriesSettings.SEASONALITY_TO_SHINGLE_RATIO),
             randomIntBetween(1, 1000),
             null,
@@ -1069,7 +1069,7 @@ public void testNullFixedValue() throws IOException {
                 TestHelpers.randomUser(),
                 null,
                 new ImputationOption(ImputationMethod.FIXED_VALUES, null),
-                randomIntBetween(1, 10000),
+                randomIntBetween(2, 10000),
                 randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
                 randomIntBetween(1, 1000),
                 null,
diff --git a/src/test/java/org/opensearch/ad/rest/ADRestTestUtils.java b/src/test/java/org/opensearch/ad/rest/ADRestTestUtils.java
index d2ea89d10..4068e125b 100644
--- a/src/test/java/org/opensearch/ad/rest/ADRestTestUtils.java
+++ b/src/test/java/org/opensearch/ad/rest/ADRestTestUtils.java
@@ -220,7 +220,7 @@ public static Response createAnomalyDetector(
             null,
             // we don't release imputation until 2.17. Disable it in bwc first.
             null, // TestHelpers.randomImputationOption(featureList),
-            randomIntBetween(1, 10000),
+            randomIntBetween(2, 10000),
             randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
             randomIntBetween(1, 1000),
             null,
diff --git a/src/test/java/org/opensearch/ad/rest/AnomalyDetectorRestApiIT.java b/src/test/java/org/opensearch/ad/rest/AnomalyDetectorRestApiIT.java
index 473152fc8..0ae223c7b 100644
--- a/src/test/java/org/opensearch/ad/rest/AnomalyDetectorRestApiIT.java
+++ b/src/test/java/org/opensearch/ad/rest/AnomalyDetectorRestApiIT.java
@@ -167,7 +167,7 @@ public void testCreateAnomalyDetectorWithDuplicateName() throws Exception {
             TestHelpers.randomUser(),
             null,
             TestHelpers.randomImputationOption(featureList),
-            randomIntBetween(1, 10000),
+            randomIntBetween(2, 10000),
             randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
             randomIntBetween(1, 1000),
             null,
@@ -367,7 +367,7 @@ public void testUpdateAnomalyDetector_disableFlattenResultIndex_shouldDeletePipe
             detector.getUser(),
             detector.getCustomResultIndexOrAlias(),
             TestHelpers.randomImputationOption(features),
-            randomIntBetween(1, 10000),
+            randomIntBetween(2, 10000),
             randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
             randomIntBetween(1, 1000),
             null,
@@ -434,7 +434,7 @@ public void testUpdateAnomalyDetectorFlattenResultIndexField() throws Exception
             detector.getUser(),
             detector.getCustomResultIndexOrAlias(),
             TestHelpers.randomImputationOption(features),
-            randomIntBetween(1, 10000),
+            randomIntBetween(2, 10000),
             randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
             randomIntBetween(1, 1000),
             detector.getRules(),
@@ -563,7 +563,7 @@ public void testUpdateAnomalyDetectorCategoryField() throws Exception {
             detector.getUser(),
             null,
             TestHelpers.randomImputationOption(features),
-            randomIntBetween(1, 10000),
+            randomIntBetween(2, 10000),
             randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
             randomIntBetween(1, 1000),
             null,
@@ -631,7 +631,7 @@ public void testUpdateAnomalyDetector() throws Exception {
             detector.getUser(),
             null,
             TestHelpers.randomImputationOption(features),
-            randomIntBetween(1, 10000),
+            randomIntBetween(2, 10000),
             randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
             randomIntBetween(1, 1000),
             null,
@@ -704,7 +704,7 @@ public void testUpdateAnomalyDetectorNameToExisting() throws Exception {
             detector1.getUser(),
             null,
             TestHelpers.randomImputationOption(features),
-            randomIntBetween(1, 10000),
+            randomIntBetween(2, 10000),
             randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
             randomIntBetween(1, 1000),
             null,
@@ -754,7 +754,7 @@ public void testUpdateAnomalyDetectorNameToNew() throws Exception {
             detector.getUser(),
             null,
             TestHelpers.randomImputationOption(features),
-            randomIntBetween(1, 10000),
+            randomIntBetween(2, 10000),
             randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
             randomIntBetween(1, 1000),
             null,
@@ -810,7 +810,7 @@ public void testUpdateAnomalyDetectorWithNotExistingIndex() throws Exception {
             detector.getUser(),
             null,
             TestHelpers.randomImputationOption(features),
-            randomIntBetween(1, 10000),
+            randomIntBetween(2, 10000),
             randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
             randomIntBetween(1, 1000),
             null,
@@ -1196,7 +1196,7 @@ public void testUpdateAnomalyDetectorWithRunningAdJob() throws Exception {
             detector.getUser(),
             null,
             TestHelpers.randomImputationOption(features),
-            randomIntBetween(1, 10000),
+            randomIntBetween(2, 10000),
             randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
             randomIntBetween(1, 1000),
             null,
diff --git a/src/test/java/org/opensearch/ad/rest/HistoricalAnalysisRestApiIT.java b/src/test/java/org/opensearch/ad/rest/HistoricalAnalysisRestApiIT.java
index a7cf87c67..32515c7f4 100644
--- a/src/test/java/org/opensearch/ad/rest/HistoricalAnalysisRestApiIT.java
+++ b/src/test/java/org/opensearch/ad/rest/HistoricalAnalysisRestApiIT.java
@@ -343,7 +343,7 @@ private AnomalyDetector randomAnomalyDetector(AnomalyDetector detector) {
             detector.getUser(),
             detector.getCustomResultIndexOrAlias(),
             detector.getImputationOption(),
-            randomIntBetween(1, 10000),
+            randomIntBetween(2, 10000),
             randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
             randomIntBetween(1, 1000),
             null,
diff --git a/src/test/java/org/opensearch/ad/rest/SecureADRestIT.java b/src/test/java/org/opensearch/ad/rest/SecureADRestIT.java
index 401ed4630..fc3b4f85a 100644
--- a/src/test/java/org/opensearch/ad/rest/SecureADRestIT.java
+++ b/src/test/java/org/opensearch/ad/rest/SecureADRestIT.java
@@ -257,7 +257,7 @@ public void testUpdateApiFilterByEnabledForAdmin() throws IOException {
             ),
             null,
             aliceDetector.getImputationOption(),
-            randomIntBetween(1, 10000),
+            randomIntBetween(2, 10000),
             randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
             randomIntBetween(1, 1000),
             null,
@@ -313,7 +313,7 @@ public void testUpdateApiFilterByEnabled() throws IOException {
             ),
             null,
             aliceDetector.getImputationOption(),
-            randomIntBetween(1, 10000),
+            randomIntBetween(2, 10000),
             randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
             randomIntBetween(1, 1000),
             null,
diff --git a/src/test/java/org/opensearch/ad/transport/AnomalyResultTransportActionTests.java b/src/test/java/org/opensearch/ad/transport/AnomalyResultTransportActionTests.java
index b3d30d5cb..542708f25 100644
--- a/src/test/java/org/opensearch/ad/transport/AnomalyResultTransportActionTests.java
+++ b/src/test/java/org/opensearch/ad/transport/AnomalyResultTransportActionTests.java
@@ -220,7 +220,7 @@ private AnomalyDetector randomDetector(List<String> indices, List<Feature> featu
             null,
             null,
             TestHelpers.randomImputationOption(features),
-            randomIntBetween(1, 10000),
+            randomIntBetween(2, 10000),
             randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
             randomIntBetween(1, 1000),
             null,
@@ -252,7 +252,7 @@ private AnomalyDetector randomHCDetector(List<String> indices, List<Feature> fea
             null,
             null,
             TestHelpers.randomImputationOption(features),
-            randomIntBetween(1, 10000),
+            randomIntBetween(2, 10000),
             randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
             randomIntBetween(1, 1000),
             null,
diff --git a/src/test/java/org/opensearch/ad/transport/ForwardADTaskRequestTests.java b/src/test/java/org/opensearch/ad/transport/ForwardADTaskRequestTests.java
index f5be130a1..2bcf9003a 100644
--- a/src/test/java/org/opensearch/ad/transport/ForwardADTaskRequestTests.java
+++ b/src/test/java/org/opensearch/ad/transport/ForwardADTaskRequestTests.java
@@ -79,7 +79,7 @@ public void testNullDetectorIdAndTaskAction() throws IOException {
             randomUser(),
             null,
             TestHelpers.randomImputationOption(null),
-            randomIntBetween(1, 10000),
+            randomIntBetween(2, 10000),
             randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
             randomIntBetween(1, 1000),
             null,
diff --git a/src/test/java/org/opensearch/ad/transport/ValidateAnomalyDetectorTransportActionTests.java b/src/test/java/org/opensearch/ad/transport/ValidateAnomalyDetectorTransportActionTests.java
index 13eaaa45e..f5f2a917a 100644
--- a/src/test/java/org/opensearch/ad/transport/ValidateAnomalyDetectorTransportActionTests.java
+++ b/src/test/java/org/opensearch/ad/transport/ValidateAnomalyDetectorTransportActionTests.java
@@ -398,7 +398,7 @@ public void testValidateAnomalyDetectorWithInvalidDetectorName() throws IOExcept
             TestHelpers.randomUser(),
             null,
             TestHelpers.randomImputationOption(featureList),
-            randomIntBetween(1, 10000),
+            randomIntBetween(2, 10000),
             randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
             randomIntBetween(1, 1000),
             null,
@@ -448,7 +448,7 @@ public void testValidateAnomalyDetectorWithDetectorNameTooLong() throws IOExcept
             TestHelpers.randomUser(),
             null,
             TestHelpers.randomImputationOption(featureList),
-            randomIntBetween(1, 10000),
+            randomIntBetween(2, 10000),
             randomInt(TimeSeriesSettings.MAX_SHINGLE_SIZE / 2),
             randomIntBetween(1, 1000),
             null,