diff --git a/include/maths/CBasicStatistics.h b/include/maths/CBasicStatistics.h
index 11d6ae0676..25b0405ae2 100644
--- a/include/maths/CBasicStatistics.h
+++ b/include/maths/CBasicStatistics.h
@@ -1241,6 +1241,9 @@ class MATHS_EXPORT CBasicStatistics {
     class COrderStatisticsStack
         : public COrderStatisticsImpl<T, boost::array<T, N>, LESS>,
           private boost::addable<COrderStatisticsStack<T, N, LESS>> {
+
+        static_assert(N > 0, "N must be > 0");
+
     private:
         using TArray = boost::array<T, N>;
         using TImpl = COrderStatisticsImpl<T, TArray, LESS>;
@@ -1327,10 +1330,18 @@ class MATHS_EXPORT CBasicStatistics {
 
     public:
         explicit COrderStatisticsHeap(std::size_t n, const LESS& less = LESS{})
-            : TImpl{std::vector<T>(n, T{}), less} {}
+            : TImpl{std::vector<T>(std::max(n, std::size_t(1)), T{}), less} {
+            if (n == 0) {
+                LOG_ERROR(<< "Invalid size of 0 for order statistics accumulator");
+            }
+        }
 
         //! Reset the number of statistics to gather to \p n.
         void resize(std::size_t n) {
+            if (n == 0) {
+                LOG_ERROR(<< "Invalid resize to 0 for order statistics accumulator");
+                n = 1;
+            }
             this->clear();
             this->statistics().resize(n);
         }
diff --git a/lib/maths/CTimeSeriesDecompositionDetail.cc b/lib/maths/CTimeSeriesDecompositionDetail.cc
index b40c03125e..fa346a5f5f 100644
--- a/lib/maths/CTimeSeriesDecompositionDetail.cc
+++ b/lib/maths/CTimeSeriesDecompositionDetail.cc
@@ -1596,30 +1596,34 @@ void CTimeSeriesDecompositionDetail::CComponents::reweightOutliers(
         })};
     double numberOutliers{SEASONAL_OUTLIER_FRACTION * numberValues};
 
-    TMinAccumulator outliers{static_cast<std::size_t>(2.0 * numberOutliers)};
-    TMeanAccumulator meanDifference;
-    core_t::TTime time = startTime + dt / 2;
-    for (std::size_t i = 0; i < values.size(); ++i, time += dt) {
-        if (CBasicStatistics::count(values[i]) > 0.0) {
-            double difference{std::fabs(CBasicStatistics::mean(values[i]) - predictor(time))};
-            outliers.add({-difference, i});
-            meanDifference.add(difference);
-        }
-    }
-    outliers.sort();
-    TMeanAccumulator meanDifferenceOfOutliers;
-    for (std::size_t i = 0u; i < static_cast<std::size_t>(numberOutliers); ++i) {
-        meanDifferenceOfOutliers.add(-outliers[i].first);
-    }
-    meanDifference -= meanDifferenceOfOutliers;
-    for (std::size_t i = 0; i < outliers.count(); ++i) {
-        if (-outliers[i].first > SEASONAL_OUTLIER_DIFFERENCE_THRESHOLD *
-                                     CBasicStatistics::mean(meanDifference)) {
-            double weight{SEASONAL_OUTLIER_WEIGHT +
-                          (1.0 - SEASONAL_OUTLIER_WEIGHT) *
-                              CTools::logisticFunction(static_cast<double>(i) / numberOutliers,
-                                                       0.1, 1.0)};
-            CBasicStatistics::count(values[outliers[i].second]) *= weight;
+    if (numberOutliers > 1.0) {
+
+        TMinAccumulator outliers{static_cast<std::size_t>(2.0 * numberOutliers)};
+        TMeanAccumulator meanDifference;
+        core_t::TTime time = startTime + dt / 2;
+        for (std::size_t i = 0; i < values.size(); ++i, time += dt) {
+            if (CBasicStatistics::count(values[i]) > 0.0) {
+                double difference{
+                    std::fabs(CBasicStatistics::mean(values[i]) - predictor(time))};
+                outliers.add({-difference, i});
+                meanDifference.add(difference);
+            }
+        }
+        outliers.sort();
+        TMeanAccumulator meanDifferenceOfOutliers;
+        for (std::size_t i = 0u; i < static_cast<std::size_t>(numberOutliers); ++i) {
+            meanDifferenceOfOutliers.add(-outliers[i].first);
+        }
+        meanDifference -= meanDifferenceOfOutliers;
+        for (std::size_t i = 0; i < outliers.count(); ++i) {
+            if (-outliers[i].first > SEASONAL_OUTLIER_DIFFERENCE_THRESHOLD *
+                                         CBasicStatistics::mean(meanDifference)) {
+                double weight{SEASONAL_OUTLIER_WEIGHT +
+                              (1.0 - SEASONAL_OUTLIER_WEIGHT) *
+                                  CTools::logisticFunction(static_cast<double>(i) / numberOutliers,
+                                                           0.1, 1.0)};
+                CBasicStatistics::count(values[outliers[i].second]) *= weight;
+            }
         }
     }
 }