Process Capability Measures Cp and Cpk: A JMP JSL Demostration

I am often asked about the diffence between Cp and Cpk. Usually it is followed up by a question on why there is a need for two measures. I then answer that while Cpk is the real capability, Cp reflects the potential capability that can still be achieved just by centering your process. This is a difficult concept to grasp if just verbally described, so I usually illustrate this using a graphical demostration.
This JMP script demostrates the differences between the two Process Capability Measures Cp and Cpk.

---

The JMP JSL Script

dlg = Dialog(
 V List(
  V List(
   "Cp Parameters",
   "",
   Line Up( 2,  
    /*"Mean", mu = Edit Number(0),*/
    "Standard Deviation", sigma = Edit Number( 1 )
   ),
   "",
   "",
   "Define Specifications",
   "",
   Line Up( 2, "USL ", upspecs = Edit Number( 2 ) ),
   Line Up( 2, "LSL ", lowspecs = Edit Number( -2 ) )
  ),
  H List( Button( "OK" ), Button( "Cancel" ) )
 )
);


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


/*ADDED line for Cp only*/
LSL = lowspecs;
USL = upspecs;
mu = lowspecs + (upspecs - lowspecs) / 2;
mid = (upspecs - lowspecs);
/*END of added line*/


rsqrt2pi = 1 / Sqrt( 2 * Pi() );

New Window( "Process Capability Demostration",
 V List Box(
  H List Box(
   Panel Box( "Cpk Window",
   T1=Text Box ("Move the Handle in the curve to change the value of the Mean"),
    g1 = Graph Box(
     FrameSize( 425, 400 ),
     X Scale( mu - 8 * sigma, mu + 8 * sigma ),
     Y Scale( 0, 1.40 * rsqrt2pi / sigma ),
     Double Buffer,
     Pen Color( "blue" ),
     Pen Size( 1 ),
     Text Size( 12 ),
     Text Color( "black" ),
     Y Function( Normal Density( (x - mu) / sigma ) / sigma, x );   /*Y-scale is Normalized to Z-scores*/
     Y Function(
      Normal Density( (x - mu) / sigma ) / sigma,
      x,
      fill( 20 ),
      Max( LSL )
     );  /*Fill low*/
     Y Function(
      Normal Density( (x - mu) / sigma ) / sigma,
      x,
      fill( 20 ),
      Min( USL )
     );  /*Fill high*/
     Pen Color( "red" );,
     Pen Size( 1 ),
     Text Size( 10 ),
     Text Color( "black" ),
     X Function( LSL, y );
     Handle( mu, rsqrt2pi / sigma, mu = x;g2<<reshow; );
     g2 << reshow;
     Handle( LSL, 0.45 * rsqrt2pi / sigma, LSL = x );
     g2 << reshow;
     Handle( USL, 0.45 * rsqrt2pi / sigma, USL = x );
     X Function( USL, y );
     delta = mu - LSL;
     Text( {mu, 0.85 * rsqrt2pi / sigma}, "mu ", mu, "  sigma ", sigma );
     Text Color( "red" );
     Text( {LSL, 0.45 * rsqrt2pi / sigma}, "LSL= ", LSL );
     Text( {USL, 0.55 * rsqrt2pi / sigma}, "USL= ", USL );
     Pen Color( "blue" );,
     Pen Size( 1 ),
     Text Size( 11 ),
     Text Color( "blue" ),
     Cp = (USL - LSL) / (6 * sigma);
     Cpu = (USL - mu) / (3 * sigma);
     Zu = (USL - mu) / sigma;
     Zl = (LSL - mu) / sigma;
     yield = Normal Distribution( Zu ) - Normal Distribution( Zl );
     Cpl = (mu - LSL) / (3 * sigma);
     Cpk = Min( Cpu, Cpl );
     Text( {mu, 1.25 * rsqrt2pi / sigma}, "Cpk= ", Cpk );
     Text( {mu, 1.15 * rsqrt2pi / sigma}, "Cp= ", Cp );
     Text( {mu, 1.05 * rsqrt2pi / sigma}, "Estimated Yield= ", yield );
    )              /* Close Graph Box parenthesis*/
   ),
   Panel Box( "Cp Window",
   T2=Text Box ("Move the Handle in the curve to change the value of the Sigma");,
    g2 = Graph Box(
     FrameSize( 425, 400 ),
     X Scale( mu - 8 * sigma, mu + 8 * sigma ),
     Y Scale( 0, 1.40 * rsqrt2pi / sigma ),
     Double Buffer,
     Handle( mu, rsqrt2pi / sigma, sigma = rsqrt2pi / y; g1<<reshow; );
     delta = mu - LSL;
     USL2 = mu + delta;
     Pen Color( "red" );,
     Pen Size( 1 ),
     Text Size( 10 ),
     Text Color( "black" ),
     X Function( LSL, y );
     X Function( USL2, y );
     Text( {mu, 0.85 * rsqrt2pi / sigma}, "mu ", mu, "  sigma ", sigma );
     Text Color( "red" );
     Text( {LSL, 0.45 * rsqrt2pi / sigma}, "LSL= ", LSL );
     Text( {USL2, 0.55 * rsqrt2pi / sigma}, "USL= ", USL2 );
     Pen Color( "blue" );,
     Pen Size( 1 ),
     Text Size( 11 ),
     Text Color( "blue" ),
     Cpu = (USL2 - mu) / (3 * sigma);
     Zu = (USL2 - mu) / sigma;
     Zl = (LSL - mu) / sigma;
     yield2 = Normal Distribution( Zu ) - Normal Distribution( Zl );
     Cpl = (mu - LSL) / (3 * sigma);
     Cp2 = (USL2 - LSL) / (6 * sigma);
     Text( {mu, 1.15 * rsqrt2pi / sigma}, "Cp= ", Cp2 );
     Text( {mu, 1.05 * rsqrt2pi / sigma}, "Estimated Yield= ", yield2 );
     Pen Color( "blue" );,
     Pen Size( 1 ),
     Text Size( 12 ),
     Text Color( "black" ),
     Y Function( Normal Density( (x - mu) / sigma ) / sigma, x );   /*Y-scale is Normalized to Z-scores*/
     Y Function(
      Normal Density( (x - mu) / sigma ) / sigma,
      x,
      fill( 20 ),
      Max( LSL )
     );  /*Fill low*/
     Y Function(
      Normal Density( (x - mu) / sigma ) / sigma,
      x,
      fill( 20 ),
      Min( USL2 )
     );  /*Fill high*/
    )
   )
  )
 )/*END Of BORDER BOX*/
);          /* Close New Window parenthesis*/

T1<<Text Color("BLUE");
T2<<Text Color("BLUE");