Sigma Level as a Measure of Process Capabiltity (Reposted from www.SixSigmaPractice.multiply.com

There are many available measures of Process Capability.
In fact anything that relates process variation to specification
limits,and measures how often the process meets these specifications can be considered as a measure of Process Capability.
Process Capability can be measured either by Percent Yield, Percent Defect, Cp, Pp, Cpk, Ppk, or Sigma Level. This JSL script uses JMP's graphical capability to demostrate how the standard Normal Curve defines the relationships between the Sigma Level, percent Yield, and percent defect.
　
Note: You may use freely but the author will appreciate it the author will be given credit, and this webpage will be sited.
Reynald Francisco
http://www.sixsigmapractice.multiply.com/

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The JMP JSL Script

When the JMP script is run, an initial dialog box would prompt the user the input initial values as shown below.
Input Dialog Box:

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The output image is a graph as shown below:

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The JMP JSL Script is shown below::

dlg = Dialog(
V List(
V List(
"ENTER THE FOLLOWING INFORMATION:",
"",
V List(
"Input Option",
V List(
TestType = Radio
Buttons( "YIELD RATE", "DEFECT RATE", "SIGMA LEVEL" ),
Line Up( 2, "Input
Value ", x = Edit Number( 0.5 ) )
)
),
"",
"Note: Input Yield
Rate and Defect Rate in decimal format."
),
H List( Button( "OK" ),
Button( "Cancel" ) )
)
);

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

If(
TestType != 3 & x >= 1,
Caption( "Input Yield Rate
and Defect Rate in decimal format. Right click to close message." );
Throw(
"User cancelled" );,
TestType != 3 & x <= 0,
Caption( "Input
value is not valid. Right click to close message." );
Throw( "User
cancelled" );,
TestType == 3 & x < 0,
Caption( "Input value is
not valid. Right click to close message." );
Throw( "User cancelled" );
);

mu = 0;
sigma = 1;
rsqrt2pi = 1 / Sqrt( 2 * Pi() );

If(
TestType == 3, SigmaLevel = x,
TestType == 1, SigmaLevel =
Normal Quantile( x ),
TestType == 2, SigmaLevel = Normal Quantile( 1 - x )
);

New Window( "Sigma Level Demostration",
Graph Box(
FrameSize( 900, 500 ),
X Scale( -10, 10 ),
Y Scale( 0, 0.5 ),
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*/
If( TestType == 2,
Y
Function( Normal Density( (x - mu) / sigma ) / sigma, x, fill( 1 ), Min(
SigmaLevel ) ),
Y Function( Normal Density( (x - mu) / sigma ) / sigma, x,
fill( 1 ), Max( SigmaLevel ) )
);
Pen Color( "red" );,
Pen Size( 1
),
Text Size( 10 ),
Text Color( "black" ),
X Function( SigmaLevel, y
);
Handle( SigmaLevel, 0.45 * rsqrt2pi / sigma, SigmaLevel = x );
Text
Color( "black" );
Text( {SigmaLevel, 0.45 * rsqrt2pi / sigma}, "<--Move
this point" );
Text Color( "red" );
Text( {SigmaLevel, 0.55 * rsqrt2pi /
sigma}, "Sigma Level= ", SigmaLevel );
Pen Color( "blue" );,
Pen Size( 1
),
Text Size( 11 ),
Text Color( "blue" ),
Z = (SigmaLevel - mu) /
sigma;
Yield = Normal Distribution( Z );
Defect = (1 - Yield);
Text(
{mu, 1.15 * rsqrt2pi / sigma}, "YIELD= ", yield * 100, "%" );
Text( {mu,
1.05 * rsqrt2pi / sigma}, "DEFECT= ", defect * 100, "%" );
) /* Close Graph
Box parenthesis*/
); /* Close New Window parenthesis*/

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