procedure: use 90th percentile to estimate the completion delay

app/models/procedure.rb

@@ -1,3 +1,5 @@
+require Rails.root.join('lib', 'percentile')
+
 class Procedure < ApplicationRecord
   MAX_DUREE_CONSERVATION = 36
 
@@ -305,15 +307,15 @@ class Procedure < ApplicationRecord
   end
 
   def usual_traitement_time
-    mean_time(:en_construction_at, :processed_at)
+    percentile_time(:en_construction_at, :processed_at, 90)
   end
 
   def usual_verification_time
-    mean_time(:en_construction_at, :en_instruction_at)
+    percentile_time(:en_construction_at, :en_instruction_at, 90)
   end
 
   def usual_instruction_time
-    mean_time(:en_instruction_at, :processed_at)
+    percentile_time(:en_instruction_at, :processed_at, 90)
   end
 
   PATH_AVAILABLE = :available
@@ -421,14 +423,14 @@ class Procedure < ApplicationRecord
     true
   end
 
-  def mean_time(start_attribute, end_attribute)
+  def percentile_time(start_attribute, end_attribute, p)
     times = dossiers
       .state_termine
       .pluck(start_attribute, end_attribute)
       .map { |(start_date, end_date)| end_date - start_date }
 
     if times.present?
-      times.sum.fdiv(times.size).ceil
+      times.percentile(p).ceil
     end
   end
 end

lib/percentile.rb

@@ -0,0 +1,31 @@
+# Adapted from https://github.com/thirtysixthspan/descriptive_statistics
+
+# Copyright (c) 2010-2014 Derrick Parkhurst (derrick.parkhurst@gmail.com)
+#
+# Permission is hereby granted, free of charge, to any person obtaining a copy
+# of this software and associated documentation files (the "Software"), to deal
+# in the Software without restriction, including without limitation the rights
+# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+# copies of the Software, and to permit persons to whom the Software is
+# furnished to do so, subject to the following conditions:
+#
+# The above copyright notice and this permission notice shall be included in
+# all copies or substantial portions of the Software.
+
+class Array
+  def percentile(p)
+    values = self.sort
+
+    if values.empty?
+      return []
+    elsif values.size == 1
+      return values.first
+    elsif p == 100
+      return values.last
+    end
+
+    rank = p / 100.0 * (values.size - 1)
+    lower, upper = values[rank.floor, 2]
+    lower + (upper - lower) * (rank - rank.floor)
+  end
+end

spec/models/procedure_spec.rb

@@ -708,19 +708,31 @@ describe Procedure do
   describe '#usual_instruction_time' do
     let(:procedure) { create(:procedure) }
 
-    context 'when there is only one dossier' do
-      let(:dossier) { create(:dossier, procedure: procedure) }
-
-      context 'which is termine' do
     before do
-          dossier.accepte!
+      processed_delays.each do |delay|
-          processed_date = Time.zone.parse('12/12/2012')
+        dossier = create :dossier, :accepte, procedure: procedure
-          instruction_date = processed_date - 1.day
+        instruction_date = 1.month.ago
-          dossier.update(en_instruction_at: instruction_date, processed_at: processed_date)
+        processed_date = instruction_date + delay
+        dossier.update!(en_instruction_at: instruction_date, processed_at: processed_date)
+      end
     end
 
-        it { expect(procedure.usual_instruction_time).to eq(1.day.to_i) }
+    context 'when there are several processed dossiers' do
+      let(:processed_delays) { [1.day, 2.days, 2.days, 2.days, 2.days, 3.days, 3.days, 3.days, 3.days, 12.days] }
+
+      it 'returns a time representative of the dossier instruction delay' do
+        expect(procedure.usual_instruction_time).to be_between(3.days, 4.days)
       end
     end
+
+    context 'when there is only one processed dossier' do
+      let(:processed_delays) { [1.day] }
+      it { expect(procedure.usual_instruction_time).to eq(1.day) }
+    end
+
+    context 'where there is no processed dossier' do
+      let(:processed_delays) { [] }
+      it { expect(procedure.usual_instruction_time).to be_nil }
+    end
   end
 end