Reliability and Reliability Engineering (Supplemental)

This is a supplementary material for the entry Reliability Part1. A bulk of reliability concepts revolves around the discussion of the Weibull Distribution and its associated Hazard Function.
The Weibull Distribution Function is characterized by 3 parameters namely Beta (for the shape), Eta (for the scale), and Gamma (for the location). Here is a JMP JSL script that demonstrates how the Weibull distribution changes as each of these parameters change. The output window is shown below:

The JMP JSL Script is shown below::

Beta_value = 1.5;
Eta_value = 2.0;
Gamma_value = 0;


EXPO = Expr(
 MESSAGEBOX = New Window( "NOTICE:",
  Border Box(
   top( 10 ),
   Left( 10 ),
   Panel Box( "Read:",
    Text Box( "If the value of the shape parameter Beta = 1, the Weibull becomes an Exponential Distribution" )
   )
  )
 );
 Wait( 2 );
 MESSAGEBOX << CLOSE WINDOW;
);

TEXT_MESSAGE = "Shape parameter Beta = " || char(Beta_value) ||"; Scale parameter Eta = "  || char(Eta_value) || "; Location parameter Gamma = " || char(Gamma_value);

NON_EXPO1 = Expr(Caption( "If the value of the shape parameter Beta = 1, the Weibull becomes an Exponential Distribution. " ));
NON_EXPO2 = Expr(Caption(TEXT_MESSAGE));

Weibull_Window = New Window( "Properties of the Weibull Density and Hazard Functions",
 V List Box(
  GraphWindow = Graph(
  FrameSize(500,500), 
  Double Buffer,
   FrameSize( 500, 300 ),
   X Scale( 0, 3 ),
   Y Scale( 0, 4 ),
   Double Buffer,
   Y Function( (Beta_value / x) * (x / eta_value) ^ Beta_value * Exp( -(x / eta_value) ^ Beta_value ), x );  /* density */
   Y Function( (Beta_value / x) * (x / eta_value) ^ Beta_value, x );                /* hazard */
   Pen Size( 2 );
   Pen Color( "red" );
   Text Color ("red");
   Text Size(12);
   text({1,.7},"Weibull Probability Distribution Function",);
   Y Function(
    (Beta_value / Eta_value) * ((x - gamma_value) / eta_value) ^ (Beta_value - 1) *
    Exp( -1 * ((x - gamma_value) / eta_value) ^ Beta_value ),
    x
   );
   Pen Color( "Blue" );
   Text Color ("Blue");
   Text Size(12);
   text({0.8,1.2},"Hazard Function",);
   Y Function( (Beta_value / Eta_value) * ((x - gamma_value) / eta_value) ^ (Beta_value - 1), x );
  ),
  H List Box(
   V List Box(
    H List Box( TB1=Text Box("Shape Parameter Beta"), Text Box("  ") ),
    Slider Box(
     0,
     10,
     Beta_value,
     TEXT_MESSAGE = "Shape parameter Beta = " || char(Beta_value) ||"; Scale parameter Eta = "  || char(Eta_value) || "; Location parameter Gamma = " || char(Gamma_value);
     GraphWindow << reshow;
     Weibull_Window<<reshow;
     If( BETA_value == 1,
      NON_EXPO1,
      NON_EXPO2
     );
    )
   ),
   V List Box(
    H List Box( TB2=Text Box( " Scale Parameter Eta" ), Text Box("  ") ),
    Slider Box(
     0,
     10,
     Eta_value,
     TEXT_MESSAGE = "Shape parameter Beta = " || char(Beta_value) ||"; Scale parameter Eta = "  || char(Eta_value) || "; Location parameter Gamma = " || char(Gamma_value);
     GraphWindow << reshow;NON_EXPO2;
    )
   ),
   V List Box(
    H List Box( TB3=Text Box( " Location Parameter Gamma" ), Text Box("  ") ),
    Slider Box(
     0,
     10,
     Gamma_value,
     TEXT_MESSAGE = "Shape parameter Beta = " || char(Beta_value) ||"; Scale parameter Eta = "  || char(Eta_value) || "; Location parameter Gamma = " || char(Gamma_value);
     GraphWindow << reshow;NON_EXPO2;
    )
   )
  )
 
 )
);



TB1 << Font color( "BLUE" );
TB1 << set Font size( 10 );
TB2 << Font color( "BLUE" );
TB2 << set Font size( 10 );
TB3 << Font color( "BLUE" );
TB3 << set Font size( 10 );

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