Control Chart as a Feedback System: A JMP JSL Demostration

This script was written using SAS JMP's version 5.1.
It demostrates how a control chart can feedback any change in distribution's central tendency and/or measure of dispersion/variation.

For any feedback, kindly send it to me @ rsfrancisco at up dot edu dot com

Regards,
Reynald Francisco

---

The JMP JSL Script

/*
DETAILS,
>>SIGMA OF THE MEAN IS COMPUTED USING THE CENTRAL LIMIT THEOREM
>>CONTROL LIMITS ARE COMPUTED USING Individuals and Moving Range Method (IMR) in which each mean and sigma of the sample are treated as an individual measure/data point.
>>DATA USED IS A RANDOMLY GENRERATED NORMALLY DISTRIBUTED VARIABLE WITH MEAN = MU (user specified) AND STDEV = SIGMA (user specified).
*/

dlg = Dialog(
V List(V List("Population parameter","",
    Line Up(2,
    "Mean", mu = Edit Number(0),
    "Standard Deviation", sigma = Edit Number(1)
       ),"","",
    "Define Sampling Plan","",
   Line Up( 2,
    "Sampling Size ",n = Edit Number(5), 
    "Initial Sub-groups ",m = Edit Number(25)
   )
   ),
 H List( Button("OK"), Button("Cancel") )
));


If( dlg["Button"] == -1, Throw( "User cancelled" ) );
Remove From( dlg ); Eval List( dlg );






 rsqrt2pi = 1/sqrt(2*pi());





/*MODULE3*/


dt = New Table( "Process Data" ); 

 

col = dt << New Column( "Parameter" );

 /* add new column to object 'dt' , which is a data table. Name the new column as "Parameter". Let new column be referred to as new object 'col' */

 /*set global constants 'pmean' and 'pSD'*/

pMean = mu;
pSD = sigma;
sigmasample=sigma/sqrt(n);

 /*CREATING A MATRIX to contain Normal Random*/




x = J( m, 1, 0 );

For( i=1, i<m+1, i++,
 x[i] = mu + sigmasample * Random Normal()
);
musample=0;
For( i=1, i<m+1, i++,
musample=musample + x[i]
);
musample=musample/m;
/* ADDING THE VALUES from the MATRIX into the CREATED COLUMN in the TABLE*/
col << Values( x );

/* CREATE a new window object called 'w' */

w = New Window( "Control Chart Simulation",
 H List Box(
(Graph Box(FrameSize(313,313), XScale(mu-6.5*sigma,mu+6.5*sigma), yScale(0,1.10*rsqrt2pi/(sigma/sqrt(n))), Double Buffer,
 
 
 Handle(mu,rsqrt2pi/sigma,mu=x;sigma=rsqrt2pi/y),

 text({musample,rsqrt2pi/sigmasample},"mu_sample= ",musample,"  \!rsigmasample= ",sigmasample),

 sigmasample=sigma/sqrt(n);
 
 Pencolor("blue"),pensize(1), text size(8),TextColor("blue"),

 YFunction(Normal Density((x-mu)/sigma)/sigma, x),

 text({mu,rsqrt2pi/(pSD/sqrt(n))},"mu= ",mu,"  sigma= ",(pSD/sqrt(n))),

 Pencolor("red"),pensize(1), text size(10),TextColor("red"),
 YFunction(Normal Density((x-musample)/(pSD/sqrt(n)))/(pSD/sqrt(n)), x),  /*Y-scale is Normalized to Z-scores*/
 
 Pencolor(4),
 text({mu,rsqrt2pi/sigmasample},"mu= ",mu,"  sigma= ",sigmasample),
 YFunction(Normal Density((x-mu)/sigmasample)/sigmasample, x)  /*Y-scale is Normalized to Z-scores*/
 )),
 
 

Control Chart(
   Sample Label(Empty()),
   KSigma(3),
   Chart Col(
    :Parameter,
    Individual Measurement,
    Moving Range
   ),
   Show Zones(1),
   All Tests(1),

   SendToReport(Dispatch({}, "Control Chart", OutlineBox, 
                   Set Title("Control Chart Simulation")),
   Dispatch({"Individual Measurement of Parameter"}, 
   "Control Charts", FrameBox, Frame Size(300, 250)), 
   Dispatch({"Moving Range of Parameter"}, "1", 
   ScaleBox, {Scale(Linear), Format(Best), Min(4), Max(38), Inc(3), 
   Minor Ticks(2)}), Dispatch({"Moving Range of Parameter"}, 
   "Control Chart", FrameBox, Frame Size(300, 250)), 
   Dispatch({"Moving Range of Parameter"}, 
   "Control Charts", FrameBox, Frame Size(80, 90))),

   Alarm Script(
    Write(
     "\!rOut of Control for test ",
     qc_test,
     " in column ",
     qc_col,
     " in sample ",
     qc_sample
    )
   )
  ),

  Button Box( "End Simulation",
   w << Close Window;
   Close( dt, No Save )
  )
 )
)
;

While( 2,
 Wait(1);
 dt << Add Rows( 1 );
 col[i++] = mu + sigmasample * Random Normal();
);