Reliability and Reliability Engineering (Supplemental2)

This is another supplementary material for the entry Reliability Part1. In another entry I provided a JMP JSL script that demostrates the properties of a Weibull Distribution. In this entry I will provide a JMP JSL script that shows the properties of the Lognormal Distribution.
The Lognormal Distribution Function is characterized by 2 parameters which are the Scale and the Shape. This distribution is usually used to model Faulure Times where aging is the most dominant cause of failure. Here is a JMP JSL script that demonstrates how the Lognormal distribution changes as each of these parameters change.

The JMP JSL Script is shown below

Clear Globals();
Shap = 2;
Scal = 4;


PDF_fx = Expr( Exp( -(Log( x ) - Log( Scal )) ^ 2 / (2 * Shap ^ 2) ) / (Shap * x * Sqrt( 2 * Pi() )) );
   
Log_Window = New Window( "Properties of the LogLogistic Density and Hazard Functions",
 V List Box(
  GraphWindow = Graph(
   FrameSize( 500, 500 ),
   Double Buffer,
   FrameSize( 500, 300 ),
   X Scale( 0, 3 ),
   Y Scale( 0, 1 ),
   Double Buffer,
   A = Scal;
   B = Shap;
   TEXT_MESSAGE = "; Scale parameter A = " || Char( A ) || "; Shape parameter B = " || Char( B );
   NON_EXPO2 = Expr( Caption( TEXT_MESSAGE ) );
   Pen Size( 2 );
   Pen Color( "red" );
   Text Color( "red" );
   Text Size( 12 );
   Text( {1, .7}, "LogNormal Probability Distribution Function" );
   Y Function( PDF_fx, x );
  ),
  H List Box(
   V List Box(
    H List Box( TB1 = Text Box( " Scale Parameter A" ), Text Box( "  " ) ),
    Slider Box(
     0.0001,
     20,
     Scal,
     GraphWindow << reshow;
     Log_Window << reshow;
     A = Scal;
     B = Shap;
     TEXT_MESSAGE = "; Scale parameter A = " || Char( A ) || "; Shape parameter B = " || Char( B );
     NON_EXPO2;
    )
   ),
   V List Box(
    H List Box( TB2 = Text Box( " Shape Parameter B" ), Text Box( "  " ) ),
    Slider Box(
     0.0001,
     10,
     Shap,
     GraphWindow << reshow;
     A = Scal;
     B = Shap;
     TEXT_MESSAGE = "; Scale parameter A = " || Char( A ) || "; Shape parameter B = " || Char( B );
     NON_EXPO2;
    )
   )
  )
 )
);
TB1 << Font color( "BLUE" );
TB1 << set Font size( 10 );
TB2 << Font color( "BLUE" );
TB2 << set Font size( 10 );