QCWestgardRules Routine

Summary

Compares values agains Westgard rules.

Declaration

Procedure QCWestgardRules(Data: TVec; OutControl: TVec; mean, sigma: TSample);

Parameter	Description
Data	Data to-be-checked with Westgard rules.
OutOfControl	Vector storing each point status. If point(i) is out-of-control, then OutControl.Values[i] will be greater than zero (see explanation above).
mean	In most cases equal to data mean, but you can specify any value.
sigma	In most cases equal to data standard deviation, but you can specify any value.

Description

Data individual values are tested to determine if they are in, or out, of control using a set of five rules called the Westgard rules. These rules indicate which points are out-of-control. The Westgard rules are (see www.westgard.com/mltirule.htm for details):

1S3: One value beyond three sigma from the mean.
1S2: One value beyond two sigma from the mean.
2S2: Two consecutive values either greater than, or less than, two sigma from the mean.
RS4: A difference between consecutive values greater than four sigma.
41S: Four consecutive values greater than, or less than, one sigma from the mean.
10X: Ten consecutive values all greater than, or less than, the mean.

For each point several rules can be violated at the same time. Each Westgard rule violation has different value:

1S3 = 1
1S2 = 2
2S2 = 4
RS4 = 8
4S1 = 16
10X = 32

For example, if rules 2S2 and 10X were violated, then the sum of violations for point would be 2 + 16 = 18.

Example 1

Load process data, then check if any points are out-of-control.

  Uses MtxExpr, StatControlCharts;
  procedure Example;
  var data, outofcontrol,indexes: Vector;
  begin
    data.LoadFromFile('process_data.vec');
    QCWestgardRules(data,outofcontrol,data.mean,data.stddev);
    // Now find indexes of out-of-control points
    indexes.FindIndexes(outofcontrol,'>',0);
    // indexes.IValues now stores the indices of out-of-control points
  end;

  #include "MtxVecCpp.h"
  #include "MathExpr.hpp"
  #include "StatControlCharts.hpp"
  void __fastcall Example()
  {
    Vector data, outofcontrol, indexes;
    data->LoadFromFile("process_data.vec");
    QCWestgardRules(data,outofcontrol,data->Mean(),data->StdDev());
    // Now find indexes of out-of-control points
    indexes->FindIndexes(outofcontrol,">",0);
    // indexes->IValues now stores the indices of out-of-control points
  }

  using Dew.Math;
  using Dew.Math.Units;
  using Dew.Stats.Units;
  namespace Dew.Examples
  {
    private void Example(Dew.Stats.QCSeries QCSeries1)
    {
      Vector data = new Vector(0);
      Vector outofcontrol = new Vector(0);
      Vector indexes = new Vector(0);
      data.LoadFromFile("process_data.vec");
      StatControlCharts.QCWestgardRules(data,outofcontrol,data.Mean(),data.StdDev());
      // Now find indexes of out-of-control points
      indexes.FindIndexes(outofcontrol,">",0);
      // indexes.IValues now stores the indices of out-of-control points
    }
  }