diff --git a/ax/analysis/healthcheck/healthcheck_analysis.py b/ax/analysis/healthcheck/healthcheck_analysis.py
index 22b5e638f1b..1e3eac451cf 100644
--- a/ax/analysis/healthcheck/healthcheck_analysis.py
+++ b/ax/analysis/healthcheck/healthcheck_analysis.py
@@ -5,11 +5,14 @@
 
 # pyre-strict
 
+from __future__ import annotations
+
 import json
 from enum import IntEnum
 
 import pandas as pd
-from ax.core.analysis_card import AnalysisCard
+from ax.analysis.analysis import ErrorAnalysisCard
+from ax.core.analysis_card import AnalysisCard, AnalysisCardBase
 
 
 class HealthcheckStatus(IntEnum):
@@ -18,6 +21,13 @@ class HealthcheckStatus(IntEnum):
     WARNING = 2
 
 
+# Healthchecks that provide valuable progress info even when passing
+PRIORITY_HEALTHCHECKS: set[str] = {
+    "BaselineImprovementAnalysis",
+    "EarlyStoppingAnalysis",
+}
+
+
 class HealthcheckAnalysisCard(AnalysisCard):
     def get_status(self) -> HealthcheckStatus:
         return HealthcheckStatus(json.loads(self.blob)["status"])
@@ -49,3 +59,49 @@ def create_healthcheck_analysis_card(
             }
         ),
     )
+
+
+# Status order for sorting: FAIL first, then WARNING, then PASS
+_STATUS_SORT_ORDER: dict[HealthcheckStatus, int] = {
+    HealthcheckStatus.FAIL: 1,
+    HealthcheckStatus.WARNING: 2,
+    HealthcheckStatus.PASS: 3,
+}
+
+
+def sort_healthcheck_cards(
+    cards: list[AnalysisCardBase],
+) -> list[AnalysisCardBase]:
+    """
+    Sort healthcheck cards by severity and priority.
+
+    Order:
+        1. ErrorAnalysisCard (errors during computation)
+        2. FAIL status
+        3. WARNING status
+        4. PASS status with priority (BaselineImprovement, EarlyStopping, etc.)
+        5. PASS status (rest)
+
+    Args:
+        cards: List of analysis cards (typically HealthcheckAnalysisCard or
+            ErrorAnalysisCard instances).
+
+    Returns:
+        Sorted list of cards.
+    """
+
+    def sort_key(card: AnalysisCardBase) -> tuple[int, int, str]:
+        if isinstance(card, ErrorAnalysisCard):
+            return (0, 0, card.name)
+
+        if isinstance(card, HealthcheckAnalysisCard):
+            return (
+                _STATUS_SORT_ORDER[card.get_status()],
+                0 if card.name in PRIORITY_HEALTHCHECKS else 1,
+                card.name,
+            )
+
+        # Fallback for type safety (unreachable in practice)
+        return (4, 1, card.name)
+
+    return sorted(cards, key=sort_key)
diff --git a/ax/analysis/healthcheck/tests/test_healthcheck_analysis.py b/ax/analysis/healthcheck/tests/test_healthcheck_analysis.py
new file mode 100644
index 00000000000..07639b71eab
--- /dev/null
+++ b/ax/analysis/healthcheck/tests/test_healthcheck_analysis.py
@@ -0,0 +1,51 @@
+# Copyright (c) Meta Platforms, Inc. and affiliates.
+#
+# This source code is licensed under the MIT license found in the
+# LICENSE file in the root directory of this source tree.
+
+# pyre-strict
+
+import pandas as pd
+from ax.analysis.analysis import ErrorAnalysisCard
+from ax.analysis.healthcheck.healthcheck_analysis import (
+    create_healthcheck_analysis_card,
+    HealthcheckStatus,
+    sort_healthcheck_cards,
+)
+from ax.core.analysis_card import AnalysisCardBase
+from ax.utils.common.testutils import TestCase
+
+
+def _card(name: str, status: HealthcheckStatus) -> AnalysisCardBase:
+    return create_healthcheck_analysis_card(
+        name=name, title=name, subtitle=name, df=pd.DataFrame(), status=status
+    )
+
+
+def _error(name: str) -> AnalysisCardBase:
+    return ErrorAnalysisCard(
+        name=name, title=name, subtitle=name, df=pd.DataFrame(), blob=""
+    )
+
+
+class TestHealthcheckAnalysis(TestCase):
+    def test_sort_ordering(self) -> None:
+        cards: list[AnalysisCardBase] = [
+            _card("RegularAnalysis", HealthcheckStatus.PASS),
+            _card("WarningAnalysis", HealthcheckStatus.WARNING),
+            _error("ErrorAnalysis"),
+            _card("BaselineImprovementAnalysis", HealthcheckStatus.PASS),
+            _card("FailAnalysis", HealthcheckStatus.FAIL),
+        ]
+        result = sort_healthcheck_cards(cards)
+
+        self.assertEqual(
+            [c.name for c in result],
+            [
+                "ErrorAnalysis",
+                "FailAnalysis",
+                "WarningAnalysis",
+                "BaselineImprovementAnalysis",
+                "RegularAnalysis",
+            ],
+        )
diff --git a/ax/analysis/overview.py b/ax/analysis/overview.py
index d31b8674fc3..bb0f041ef77 100644
--- a/ax/analysis/overview.py
+++ b/ax/analysis/overview.py
@@ -8,7 +8,7 @@
 from typing import Any, final
 
 from ax.adapter.base import Adapter
-from ax.analysis.analysis import Analysis, ErrorAnalysisCard
+from ax.analysis.analysis import Analysis
 from ax.analysis.diagnostics import DiagnosticAnalysis
 from ax.analysis.healthcheck.baseline_improvement import BaselineImprovementAnalysis
 from ax.analysis.healthcheck.can_generate_candidates import (
@@ -19,7 +19,7 @@
     ConstraintsFeasibilityAnalysis,
 )
 from ax.analysis.healthcheck.early_stopping_healthcheck import EarlyStoppingAnalysis
-from ax.analysis.healthcheck.healthcheck_analysis import HealthcheckAnalysisCard
+from ax.analysis.healthcheck.healthcheck_analysis import sort_healthcheck_cards
 from ax.analysis.healthcheck.metric_fetching_errors import MetricFetchingErrorsAnalysis
 from ax.analysis.healthcheck.predictable_metrics import PredictableMetricsAnalysis
 from ax.analysis.healthcheck.search_space_analysis import SearchSpaceAnalysis
@@ -247,21 +247,14 @@ def compute(
             if analyis is not None
         ]
 
-        non_passing_health_checks = [
-            card
-            for card in health_check_cards
-            if (isinstance(card, HealthcheckAnalysisCard) and not card.is_passing())
-            or isinstance(card, ErrorAnalysisCard)
-        ]
-
         health_checks_group = (
             AnalysisCardGroup(
                 name="HealthchecksAnalysis",
                 title=HEALTH_CHECK_CARDGROUP_TITLE,
                 subtitle=HEALTH_CHECK_CARDGROUP_SUBTITLE,
-                children=non_passing_health_checks,
+                children=sort_healthcheck_cards(health_check_cards),
             )
-            if len(non_passing_health_checks) > 0
+            if len(health_check_cards) > 0
             else None
         )