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LazStats: Fix individuals x-bar chart to agree with JMP software. Nicer labeling of horizontal lines in the SPC charts. Calculate and display Cp, Cpk and Cpm values.

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git-svn-id: https://svn.code.sf.net/p/lazarus-ccr/svn@7665 8e941d3f-bd1b-0410-a28a-d453659cc2b4
This commit is contained in:
wp_xxyyzz
2020-09-13 22:50:54 +00:00
parent ed04056db4
commit 980c4033d0
3 changed files with 203 additions and 83 deletions
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18
applications/lazstats/source/forms/analysis/statistical_process_control/basicspcunit.pas
View File

@ -128,6 +128,8 @@ const
TOP_MARGIN = 150;
BOTTOM_MARGIN = 200;
FORMAT_MASK = '0.000';
{ TBasicSPCForm }
@ -323,7 +325,7 @@ const
TARGET_COLOR = clBlue;
CL_COLOR = clRed;
SPEC_COLOR = clGreen;
CL_STYLE = psDot;
CL_STYLE = psDash;
SPEC_STYLE = psSolid;
var
ser: TChartSeries;
@ -349,19 +351,19 @@ begin
if not IsNaN(GrandMean) then
begin
FChartFrame.HorLine(GrandMean, clRed, psSolid, AGrandMeanTitle);
rightLabels.Add(GrandMean, GrandMean, AGrandMeanTitle);
rightLabels.Add(GrandMean, GrandMean, AGrandMeanTitle + '=' + FormatFloat(FORMAT_MASK, GrandMean));
end;
if not IsNaN(UCL) then
begin
FChartFrame.HorLine(UCL, CL_COLOR, CL_STYLE, 'UCL/LCL');
rightLabels.Add(UCL, UCL, 'UCL');
rightLabels.Add(UCL, UCL, 'UCL=' + FormatFloat(FORMAT_MASK, UCL));
end;
if not IsNaN(LCL) then
begin
FChartFrame.HorLine(LCL, CL_COLOR, CL_STYLE, '');
rightLabels.Add(UCL, LCL, 'LCL');
rightLabels.Add(UCL, LCL, 'LCL=' + FormatFloat(FORMAT_MASK, LCL));
end;
if not IsNan(UpperSpec) then
@ -371,12 +373,12 @@ begin
else
s := 'Upper/Lower Spec';
FChartFrame.HorLine(UpperSpec, SPEC_COLOR, SPEC_STYLE, s);
rightLabels.Add(UpperSpec, UpperSpec, 'Upper Spec');
rightLabels.Add(UpperSpec, UpperSpec, 'USL=' + FormatFloat(FORMAT_MASK, UpperSpec));
end;
if not IsNaN(TargetSpec) then begin
FChartFrame.HorLine(TargetSpec, TARGET_COLOR, psSolid, 'Target');
rightLabels.Add(TargetSpec, TargetSpec, 'Target');
rightLabels.Add(TargetSpec, TargetSpec, 'Target=' + FormatFloat(FORMAT_MASK, TargetSpec));
end;
if not IsNaN(LowerSpec) then
@ -387,8 +389,10 @@ begin
s := 'Upper/Lower Spec';
constLine := FChartFrame.HorLine(LowerSpec, SPEC_COLOR, SPEC_STYLE, s);
constLine.Legend.Visible := IsNaN(UpperSpec);
rightLabels.Add(LowerSpec, LowerSpec, 'Lower Spec');
rightLabels.Add(LowerSpec, LowerSpec, 'LSL=' + FormatFloat(FORMAT_MASK, LowerSpec));
end;
FChartFrame.Chart.Legend.Visible := false;
end;

40
applications/lazstats/source/forms/analysis/statistical_process_control/xbarchartunit.lfm
View File

@ -1,19 +1,19 @@
inherited XBarChartForm: TXBarChartForm
Left = 572
Height = 431
Height = 476
Top = 215
HelpType = htKeyword
HelpKeyword = 'html/XBarChart.htm'
Caption = 'X-Bar Control Chart'
ClientHeight = 431
ClientHeight = 476
OnActivate = FormActivate
inherited SpecsPanel: TPanel
Height = 431
Height = 476
Width = 379
ClientHeight = 431
ClientHeight = 476
ClientWidth = 379
inherited ButtonPanel: TPanel
Top = 389
Top = 434
Width = 379
ClientWidth = 379
TabOrder = 5
@ -34,7 +34,7 @@ inherited XBarChartForm: TXBarChartForm
end
end
inherited VarList: TListBox
Height = 356
Height = 401
Width = 169
end
inherited GroupLabel: TLabel
@ -121,7 +121,7 @@ inherited XBarChartForm: TXBarChartForm
AnchorSideRight.Control = MeasEdit
AnchorSideRight.Side = asrBottom
Left = 177
Height = 103
Height = 128
Top = 293
Width = 202
Anchors = [akTop, akLeft, akRight]
@ -129,7 +129,7 @@ inherited XBarChartForm: TXBarChartForm
BorderSpacing.Top = 12
BorderSpacing.Bottom = 8
Caption = 'Show...'
ClientHeight = 83
ClientHeight = 108
ClientWidth = 198
TabOrder = 4
object UpperSpecChk: TCheckBox
@ -218,26 +218,38 @@ inherited XBarChartForm: TXBarChartForm
TabOrder = 5
Text = 'TargetSpecEdit'
end
object ZonesChk: TCheckBox
AnchorSideLeft.Control = TargetChk
AnchorSideTop.Control = TargetSpecEdit
AnchorSideTop.Side = asrBottom
Left = 12
Height = 19
Top = 81
Width = 52
BorderSpacing.Bottom = 8
Caption = 'Zones'
TabOrder = 6
end
end
end
inherited SpecsSplitter: TSplitter
Left = 390
Height = 431
Height = 476
end
inherited PageControl: TPageControl
Left = 398
Height = 419
Height = 464
Width = 523
inherited ReportPage: TTabSheet
ClientHeight = 391
ClientHeight = 436
ClientWidth = 515
inherited Panel1: TPanel
Height = 351
Height = 396
Width = 503
ClientHeight = 347
ClientHeight = 392
ClientWidth = 499
inherited ReportMemo: TMemo
Height = 339
Height = 384
Width = 491
end
end

228
applications/lazstats/source/forms/analysis/statistical_process_control/xbarchartunit.pas
View File

@ -1,3 +1,20 @@
{ This unit was checked against the commercial statistical package JMP and
creates correct results.
Data file for testing: "boltsize.laz"
Group variable: LotNo
Selected variable: BoltLngth
The original LazStats help files suggest
Upper Spec Level 20.05
Lower Spec Level 19.95
Target Spec 20.00
but this would indicate a very poor process. Better values:
Upper Spec Level 21.00
Lower Spec Level 19.00
Target Spec 20.00
}
unit XBarChartUnit;
{$mode objfpc}{$H+}
@ -6,13 +23,15 @@ interface
uses
Classes, SysUtils, Forms, Controls, Graphics, Dialogs, ComCtrls,
ExtCtrls, StdCtrls, BasicSPCUnit;
ExtCtrls, StdCtrls, Buttons, PrintersDlgs,
Globals, BasicSPCUnit;
type
{ TXBarChartForm }
TXBarChartForm = class(TBasicSPCForm)
ZonesChk: TCheckBox;
LevelOptns: TGroupBox;
LowerSpecChk: TCheckBox;
LowerSpecEdit: TEdit;
@ -23,8 +42,13 @@ type
UpperSpecEdit: TEdit;
XSigmaEdit: TEdit;
procedure FormActivate(Sender: TObject);
private
FAveStdDev: Double;
protected
procedure Compute; override;
procedure PlotMeans(ATitle, AXTitle, AYTitle, ADataTitle, AGrandMeanTitle: String;
const Groups: StrDyneVec; const Means: DblDyneVec;
UCL, LCL, GrandMean, TargetSpec, LowerSpec, UpperSpec: double); override;
procedure Reset; override;
function Validate(out AMsg: String; out AControl: TWinControl): Boolean; override;
end;
@ -37,7 +61,7 @@ implementation
uses
Math,
Globals, Utils, MainUnit, DataProcs;
Utils, MainUnit, DataProcs;
{$R *.lfm}
@ -80,15 +104,19 @@ var
upperSpec: Double = NaN;
lowerSpec: Double = NaN;
targetSpec: Double = NaN;
Cp: Double = NaN;
Cpk: Double = NaN;
Cpm: Double = NaN;
ColNoSelected: IntDyneVec = nil;
groups: StrDyneVec = nil;
means: DblDyneVec = nil;
stdDev: DblDyneVec = nil;
count: IntDyneVec = nil;
numGrps, grpIndex, totalNumCases, grpSize: Integer;
numValues, numGrps, grpIndex, grpSize: Integer;
grp: String;
X, Xsq: Double;
sigma, aveStdDev, UCL, LCL, grandMean, grandSD, SEMean, C4Value: Double;
X, Xsq, prevX: Double;
sigma, UCL, LCL, grandMean, grandSD, SEMean: Double;
individualsChart: Boolean;
lReport: TStrings;
begin
if GroupEdit.Text <> '' then
@ -96,10 +124,12 @@ begin
SetLength(ColNoSelected, 2);
ColNoSelected[0] := GrpVar;
ColNoSelected[1] := MeasVar;
individualsChart := false;
end else
begin
SetLength(ColNoSelected, 1);
ColNoSelected[0] := MeasVar;
individualsChart := true;
end;
if UpperSpecChk.Checked and (UpperSpecEdit.Text <> '') then
@ -117,71 +147,83 @@ begin
else raise Exception.Create('Sigma case not handled.');
end;
if GroupEdit.Text = '' then
if individualsChart then
SetLength(groups, NoCases)
else
groups := GetGroups;
numGrps := Length(groups);
SetLength(means, numGrps);
SetLength(count, numGrps);
SetLength(stddev, numGrps);
SEMean := 0.0;
grandMean := 0.0;
totalNumCases := 0;
grandSD := 0.0;
numValues := 0;
// calculate group means, grand mean, group sd's, seMean
for i := 1 to NoCases do
// calculate group means, grand mean, group std devs, seMean
if IndividualsChart then
begin
if not GoodRecord(i, Length(ColNoSelected), ColNoSelected) then continue;
if GroupEdit.Text = '' then
// x-bar chart of individual measurements, no groups
SetLength(count, 0); // not needed, count is always 1
prevX := NaN;
for i := 1 to NoCases do
begin
// individuals x-bar chart
grpIndex := totalNumCases;
if not GoodRecord(i, Length(ColNoSelected), ColNoSelected) then continue;
grpIndex := numValues; // is counted up in this loop
X := StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[MeasVar, i]));
Xsq := X*X;
groups[grpIndex] := IntToStr(i);
end else
means[grpIndex] := means[grpIndex] + X;
if not IsNaN(prevX) then
stddev[grpIndex-1] := abs(X - prevX); // assume std dev to be moving range;
// -1 --> skip empty 1st value
grandMean := grandMean + X;
grandSD := grandSD + Xsq;
inc(numValues);
prevX := X;
end;
end else
begin
// grouped x-bar chart
SetLength(count, numGrps);
for i := 1 to NoCases do
begin
// grouped x-bar chart
if not GoodRecord(i, Length(ColNoSelected), ColNoSelected) then continue;
grp := Trim(OS3MainFrm.DataGrid.Cells[GrpVar, i]);
grpIndex := IndexOfString(groups, grp);
X := StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[MeasVar, i]));
Xsq := X*X;
inc(count[grpIndex]);
means[grpIndex] := means[grpIndex] + X;
stddev[grpIndex] := stddev[grpIndex] + Xsq;
grandMean := grandMean + X;
grandSD := grandSD + Xsq;
inc(numValues);
end;
X := StrToFloat(Trim(OS3MainFrm.DataGrid.Cells[MeasVar, i]));
Xsq := X*X;
inc(count[grpIndex]);
means[grpIndex] := means[grpIndex] + X;
stddev[grpIndex] := stddev[grpIndex] + Xsq;
grandMean := grandMean + X;
SEMean := SEMean + Xsq;
inc(totalNumCases);
end;
SEMean := SEMean - sqr(grandMean) / totalNumCases;
SEMean := sqrt(SEMean / (totalNumCases - 1));
grandSD := SEMean;
SEMean := SEMean / sqrt(totalNumCases);
grandMean := grandMean / totalNumCases;
grandSD := grandSD - sqr(grandMean) / numValues;
grandSD := sqrt(grandSD / (numValues - 1));
SEMean := grandSD / sqrt(numValues);
grandMean := grandMean / numValues;
if (GroupEdit.Text = '') then
if individualsChart then
begin
// Individuals chart
grpSize := 1;
SetLength(means, totalNumCases);
SetLength(stddev, totalNumCases);
Setlength(count, totalNumCases);
for i := 0 to totalNumCases-1 do
stddev[i] := SEMean;
aveStdDev := NaN;
if totalNumCases <= 25 then
C4Value := C4[totalNumCases]
else
C4Value := 1.0;
UCL := grandMean + sigma * grandSD / C4Value;
LCL := grandMean - sigma * grandSD / C4Value;
SetLength(means, numValues);
Setlength(count, numValues);
SetLength(stddev, numValues-1); // -1 for the missing 1st value
FAveStdDev := 0;
for i := 0 to High(stddev) do
FAveStdDev := FAveStdDev + stdDev[i];
FAveStdDev := FAveStdDev / Length(stddev) / 1.128; // 1.128 is the value of d2 fo n = 2.
UCL := grandMean + sigma * FAveStdDev;
LCL := grandMean - sigma * FAveStdDev;
end else
begin
// Grouped chart
// Check group size - it is assumed that all groups are equally sized
// Check group size first; it is assumed that all groups are equally sized
grpSize := count[0];
for i := 1 to numGrps-1 do
if count[i] <> grpSize then
@ -190,9 +232,10 @@ begin
exit;
end;
aveStdDev := aveStdDev + stdDev[i];
aveStdDev := 0;
SetLength(means, numGrps);
Setlength(count, numGrps);
SetLength(stddev, numGrps);
FAveStdDev := 0;
for i := 0 to numGrps-1 do
begin
if count[i] = 0 then
@ -206,40 +249,71 @@ begin
else
begin
stddev[i] := stddev[i] - sqr(means[i]) / count[i];
stddev[i] := stddev[i] / (count[i] - 1); // Variance of group i
aveStdDev := aveStdDev + stdDev[i]; // Sum of variances
stddev[i] := sqrt(stddev[i]); // StdDev of group i
stddev[i] := stddev[i] / (count[i] - 1); // Variance of group i
FAveStdDev := FAveStdDev + stdDev[i]; // Sum of variances
stddev[i] := sqrt(stddev[i]); // StdDev of group i
end;
means[i] := means[i] / count[i];
end;
end;
aveStdDev := sqrt(aveStdDev / (numGrps * grpSize));
UCL := grandMean + sigma * aveStdDev;
LCL := grandMean - sigma * aveStdDev;
FAveStdDev := sqrt(FAveStdDev / (numGrps * grpSize));
UCL := grandMean + sigma * FAveStdDev;
LCL := grandMean - sigma * FAveStdDev;
//UCL := grandMean + sigma * grandSD / sqrt(grpSize); // this works, too, a bit more off of JMP than the above...
//LCL := grandMean - sigma * grandSD / sqrt(grpSize);
// UCL := grandMean + sigma * SEMean; // old LazStats calculation -- does not agree with JMP software.
// LCL := grandMean - sigma * SEMean;
end;
// Print results
if not IsNaN(upperSpec) and not IsNaN(lowerSpec) then
begin
Cp := (upperSpec - lowerSpec) / (6* FAveStdDev);
Cpk := Min(UpperSpec - grandMean, grandMean - LowerSpec) / (3 * FAveStdDev);
if not IsNaN(targetSpec) then
Cpm := (upperSpec - lowerSpec) / (6 * sqrt(sqr(FAveStdDev) + sqr(grandMean - targetSpec)));
end;
// Print results
lReport := TStringList.Create;
try
lReport.Add('X BAR CHART RESULTS');
lReport.Add('');
lReport.Add('Number of values: %8d', [totalNumCases]);
lReport.Add('Number of values: %8d', [numValues]);
lReport.Add('Number of groups: %8d', [numGrps]);
lReport.Add('Group size: %8d', [grpSize]);
lReport.Add('');
lReport.Add('Grand Mean: %8.3f', [grandMean]);
lReport.Add('Standard Deviation: %8.3f', [grandSD]);
lReport.Add('Standard Error of Mean: %8.3f', [SEMean]);
lReport.Add('Average Std Deviation: %8.3f', [aveStdDev]);
lReport.Add('Lower Control Limit: %8.3f', [LCL]);
lReport.Add('Average Std Deviation: %8.3f', [FAveStdDev]);
lReport.Add('Upper Control Limit: %8.3f', [UCL]);
lReport.Add('Lower Control Limit: %8.3f', [LCL]);
lReport.Add('');
lReport.Add(' Group Size Mean Std.Dev.');
lReport.Add('------- ---- -------- --------');
for i := 0 to numGrps-1 do
lReport.Add('%7s %4d %8.2f %8.2f', [groups[i], count[i], means[i], stddev[i]]);
if not IsNaN(targetSpec) then
lReport.Add('Target: %8.3f', [targetSpec]);
if not IsNaN(upperSpec) then
lReport.Add('Upper Spec Limit: %8.3f', [upperSpec]);
if not IsNaN(lowerSpec) then
lReport.Add('Lower Spec Limit: %8.3f', [lowerSpec]);
if not IsNaN(Cp) then
lReport.Add('Cp: %8.3f', [cp]);
if not IsNaN(Cpk) then
lReport.Add('Cpk: %8.3f', [Cpk]);
if not IsNaN(Cpm) then
lReport.Add('Cpm: %8.3f', [Cpm]);
lReport.Add('');
lReport.Add(' Group Size Mean Std.Dev.');
lReport.Add('------- ---- -------- --------');
if individualsChart then
begin
lReport.Add ('%7s %4d %8.2f', [groups[i], count[i], means[i]]);
for i := 1 to numGrps-1 do
lReport.Add('%7s %4d %8.2f %8.2f', [groups[i], count[i], means[i], stddev[i-1]]);
end else
for i := 0 to numGrps-1 do
lReport.Add('%7s %4d %8.2f %8.2f', [groups[i], count[i], means[i], stddev[i]]);
ReportMemo.Lines.Assign(lReport);
finally
@ -249,13 +323,42 @@ begin
// Show graph
PlotMeans(
Format('x&#772; chart for "%s"', [GetFileName]),
GroupEdit.Text, MeasEdit.Text, 'Group means', 'Grand mean',
GroupEdit.Text, MeasEdit.Text, '', 'Avg',
groups, means,
UCL, LCL, grandmean,
targetSpec, lowerSpec, upperSpec
);
end;
procedure TXBarChartForm.PlotMeans(
ATitle, AXTitle, AYTitle, ADataTitle, AGrandMeanTitle: String;
const Groups: StrDyneVec; const Means: DblDyneVec;
UCL, LCL, GrandMean, TargetSpec, LowerSpec, UpperSpec: double);
const
EPS = 1E-6;
var
y: Double;
begin
inherited;
if not ZonesChk.Checked then
exit;
y := GrandMean + FAveStdDev;
while y < UCL - EPS do
begin
FChartFrame.HorLine(y, clRed, psDot, '');
y := y + FAveStdDev;
end;
y := GrandMean - FAveStdDev;
while y > LCL + EPS do
begin
FChartFrame.HorLine(y, clRed, psDot, '');
y := y - FAveStdDev;
end;
end;
procedure TXBarChartForm.Reset;
begin
inherited;
@ -266,6 +369,7 @@ begin
UpperSpecChk.Checked := false;
LowerSpecChk.Checked := false;
TargetChk.Checked := false;
ZonesChk.Checked := false;
end;
function TXBarChartForm.Validate(out AMsg: String; out AControl: TWinControl): Boolean;