BWEHAZ

BWEHAZ (LET)

Library Function

Compute the Bi-Weibull hazard function with shape parameters SCALE1, GAMMA1, LOC2, SCALE2, and GAMMA2.

The Bi-Weibull distribution is a mixture of two Weibull distributions: a "burn-in" Weibull and a "wear out" Weibull. This makes it a very flexible distribution for reliability applications.

The hazard function for the bi-Weibull distribution is:

with s₁, , s₂, > 0 and 0.

This is a mixture of a 2-parameter Weibull (the burn-in) and a 3-parameter Weibull (the wear out). This is related to, but slightly different than, the standard Weibull mixture which is simply a weighted sum of two or more Weibull distributions.

Note that Evans, Hastings, and Peacock define the first scale parameter as the reciprocal of what we have defined above.

LET <y> = BWEHAZ(<x>,<scale1>,<gamma>,<loc2>,<scale2>,<gamma2>)
                            <SUBSET/EXCEPT/FOR qualification>
where <x> is a variable, number, or parameter;
              <y> is a variable or a parameter (depending on what <x> is) where the computed Bi-Weibull hazard value is stored;
              <scale1> is a positive number, parameter, or variable that specifies the scale parameter for the first Weibull component;
              <gamma1> is a positive number, parameter, or variable that specifies the shape parameter for the first Weibull component;
              <loc2> is a positive number, parameter, or variable that specifies the location parameter for the second Weibull component;
              <scale2> is a positive number, parameter, or variable that specifies the scale parameter for the second Weibull component;
              <gamma2> is a positive number, parameter, or variable that specifies the shape parameter for the second Weibull component;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET A = BWEHAZ(3,10,0.6,4,5,2.5)
LET A = BWEHAZ(X,S1,G1,L2,S2,G2)
PLOT BWEHAZ(X,10,0.7,4,4,3) FOR X = 0.01 0.01 15

None

None

BWECHAZ	= Compute the Bi-Weibull cumulative hazard function.
BWECDF	= Compute the Bi-Weibull cumulative distribution function.
BWEPDF	= Compute the Bi-Weibull probability density function.
BWEPPF	= Compute the Bi-Weibull percent point function.
WEIPDF	= Compute the Weibull probability density function.
EXPPDF	= Compute the exponential probability density function.
LGNPDF	= Compute the lognormal probability density function.

"Statistical Distributions", Third Edition, Evans, Hastings, and Peacock, Wiley and Sons, 2001.

Reliability Analysis

2002/5

LET SCALE1 = 10 
LET GAMMA1 = 0.7 
LET LOC2 = 4 
LET SCALE2 = 4 
LET GAMMA2 = 3 
Y1LABEL HAZARD 
X1LABEL X 
TITLE BI-WEIBULL HAZARD FUNCTION CR() ...
 S1 = ^SCALE1, G1 = ^GAMMA1, LOC2 = ^LOC2, S2 = ^SCALE2, G2 = ^GAMMA2
PLOT BWEHAZ(X,SCALE1,GAMMA1,LOC2,SCALE2,GAMMA2) FOR X = .01 .01 10