SED navigation bar go to SED home page go to Dataplot home page go to NIST home page SED Home Page SED Staff SED Projects SED Products and Publications Search SED Pages
Dataplot Vol 2 Vol 1

BWEHAZ

Name:
    BWEHAZ (LET)
Type:
    Library Function
Purpose:
    Compute the Bi-Weibull hazard function with shape parameters SCALE1, GAMMA1, LOC2, SCALE2, and GAMMA2.
Description:
    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:

      h(x,s1,gamma1,mu2,s2,gamma2) =
 (1/s1)*gamma1*(X/s1)**(gamma1-1)      0 < x < mu2
 (1/s1)*gamma1*(X/s1)**(gamma1-1) +
 (gamma2/s2)*((x-mu2)/s2)**(gamma2-1)   x >= mu2
    with s1, gamma1, s2, gamma2 > 0 and mu2 >= 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.

Syntax:
    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.
Examples:
    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
Default:
    None
Synonyms:
    None
Related Commands:
    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.
Reference:
    "Statistical Distributions", Third Edition, Evans, Hastings, and Peacock, Wiley and Sons, 2001.
Applications:
    Reliability Analysis
Implementation Date:
    2002/5
Program:
    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 
        
    plot generated by sample program

Date created: 5/31/2002
Last updated: 4/4/2003
Please email comments on this WWW page to alan.heckert@nist.gov.