Add C⁺ and C⁻ support in cusum_rules [#6]

spec/montgomery_spec.rb

@@ -190,10 +190,27 @@ class MontgomerySpec < SpcSpec
     describe "Cusum with fixed target" do
       subject do
         DB.from(
-          Sequel.lit('spc_reports.cusum_rules(?)', 10) # target mean = 10
+          Sequel.lit('spc_reports.cusum_rules(?, ?)',
+                     0.5, # allowance
+                     10 # target mean
+          )
         ).where(instrument_id:).order_by(:sample_id)
       end
 
+
+      describe "Calculating net deviation" do
+        it_has_correct_values(column: :deviation, values: [
+          # @formatter:off
+          -0.55,  -2.01,  -0.71,  1.66,   2.16,
+          0.18,   -1.96,  1.46,   -0.8,   0.34,
+          -0.97,  1.47,   0.51,   -0.6,   0.08,
+          -0.63,  0.62,   0.31,   -1.48,  0.84,
+          0.9,    -0.67,  2.29,   1.5,    0.6,
+          1.08,   0.38,   1.62,   1.31,   0.52
+        # @formatter:on
+        ])
+      end
+
       describe "Calculating Cₙ" do
         it_has_correct_values(column: :c_n, values: [
           # @formatter:off
@@ -206,6 +223,58 @@ class MontgomerySpec < SpcSpec
           # @formatter:on
         ])
       end
+
+      describe "Calculating positive deviation" do
+        it_has_correct_values(column: :deviation_plus, values: [
+          # @formatter:off
+          -1.05,  -2.51,  -1.21,  1.16,   1.66,
+          -0.32,  -2.46,  0.96,   -1.3,   -0.16,
+          -1.47,  0.97,   0.01,   -1.1,   -0.42,
+          -1.13,  0.12,   -0.19,  -1.98,  0.34,
+          0.4,    -1.17,  1.79,   1.0,    0.1,
+          0.58,   -0.12,  1.12,   0.81,   0.02
+          # @formatter:on
+        ])
+      end
+
+      describe "Calculating C⁺" do
+        it_has_correct_values(column: :c_plus, values: [
+          # @formatter:off
+          0,      0,      0,      1.16,   2.82,
+          2.50,   0.04,   1.00,   0,      0,
+          0,      0.97,   0.98,   0,      0,
+          0,      0.12,   0,      0,      0.34,
+          0.74,   0,      1.79,   2.79,   2.89,
+          3.47,   3.35,   4.47,   5.28,   5.30
+          # @formatter:on
+        ])
+      end
+
+      describe "Calculating negative deviation" do
+        it_has_correct_values(column: :deviation_minus, values: [
+          # @formatter:off
+          -0.05,  -1.51,  -0.21,  2.16,   2.66,
+          0.68,   -1.46,  1.96,   -0.3,   0.84,
+          -0.47,  1.97,   1.01,   -0.1,   0.58,
+          -0.13,  1.12,   0.81,   -0.98,  1.34,
+          1.4,    -0.17,  2.79,   2.0,    1.1,
+          1.58,   0.88,   2.12,   1.81,   1.02
+          # @formatter:on
+        ])
+      end
+
+      describe "Calculating C⁻" do
+        it_has_correct_values(column: :c_minus, values: [
+          # @formatter:off
+          -0.05,  -1.56,    -1.77,  0,      0,
+          0,      -1.46,    0,      -0.3,   0,
+          -0.47,  0,        0,      -0.1,   0,
+          -0.13,  0,        0,      -0.98,  0,
+          0,      -0.17,    0,      0,      0,
+          0,      0,        0,      0,      0
+          # @formatter:on
+        ])
+      end
     end
   end
 end

sql/02-spc-intermediates-schema.sql

@@ -508,3 +508,40 @@ $$;
 
 -- Cumulative Sum, aka Cusum
 
+create function spc_intermediates.cusum_c_plus_step(
+      last_c_plus decimal
+    , measurement decimal
+    , allowance   decimal
+    , target_mean decimal
+) returns decimal immutable language sql as
+$$
+    select greatest(coalesce(last_c_plus, 0) + (measurement - target_mean - allowance), 0);
+$$;
+
+create aggregate spc_intermediates.cusum_c_plus(
+      measurement decimal
+    , allowance decimal
+    , target_mean decimal
+) (
+    sfunc = spc_intermediates.cusum_c_plus_step,
+    stype = decimal
+);
+
+create function spc_intermediates.cusum_c_minus_step(
+      last_c_minus decimal
+    , measurement  decimal
+    , allowance    decimal
+    , target_mean  decimal
+) returns decimal immutable language sql as
+$$
+    select least(coalesce(last_c_minus, 0) + (measurement - target_mean + allowance), 0);
+$$;
+
+create aggregate spc_intermediates.cusum_c_minus(
+      measurement decimal
+    , allowance decimal
+    , target_mean decimal
+) (
+    sfunc = spc_intermediates.cusum_c_minus_step,
+    stype = decimal
+);

sql/03-spc-reports-schema.sql

@@ -395,30 +395,42 @@ $$;
 -- Cumulative Sum aka Cusum
 
 create function spc_reports.cusum_rules(
-    p_target_mean     decimal default null
+      p_allowance       decimal
+    , p_target_mean     decimal default null
 )
 returns table (
     measurement_id  bigint,
     sample_id       bigint,
     window_id       bigint,
     instrument_id   bigint,
     measured_value  decimal,
-    error           decimal,
-    C_n             decimal
+    deviation       decimal,
+    deviation_plus  decimal,
+    deviation_minus decimal,
+    C_n             decimal,
+    C_plus          decimal,
+    C_minus         decimal
 )
 immutable language sql as
 $$
       select m.id as measurement_id
     , m.sample_id
-    , w.id                                                                      as window_id
+    , w.id                                                                          as window_id
     , s.instrument_id
     , m.measured_value
-    , m.measured_value - coalesce(p_target_mean, mean_measured_value)           as error
+    , m.measured_value - coalesce(p_target_mean, mean_measured_value)               as deviation
+    , m.measured_value - coalesce(p_target_mean, mean_measured_value) - p_allowance as deviation_plus
+    , m.measured_value - coalesce(p_target_mean, mean_measured_value) + p_allowance as deviation_plus
     , sum(m.measured_value - coalesce(p_target_mean, mean_measured_value))
-        over (partition by w.id order by m.id)                                  as C_n
+        over (partition by w.id order by m.id)                                      as C_n
+    , spc_intermediates.cusum_c_plus(m.measured_value, p_allowance, coalesce(p_target_mean, mean_measured_value))
+        over window_sample                                                          as C_plus
+    , spc_intermediates.cusum_c_minus(m.measured_value, p_allowance, coalesce(p_target_mean, mean_measured_value))
+        over window_sample                                                          as C_minus
 from spc_data.measurements m
          join spc_data.samples s on s.id = m.sample_id
          join spc_data.instruments i on i.id = s.instrument_id
          join spc_data.windows w on i.id = w.instrument_id
-         join spc_intermediates.individual_measurement_statistics_ewma imse on w.id = imse.window_id;
+         join spc_intermediates.individual_measurement_statistics_ewma imse on w.id = imse.window_id
+window window_sample as (partition by w.id order by m.sample_id);
 $$;