BWEPPF

BWEPPF (LET)

Library Function

Compute the Bi-Weibull percent point 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.

For p BWECDF(), the percent point function for the bi-Weibull distribution is computed as:

with s₁, , s₂, > 0 and 0.

For BWECDF() < p < 1, the percent point function for the bi-Weibull distribution is computed numerically using a bisection method.

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> = BWEPPF(<p>,<scale1>,<gamma>,<loc2>,<scale2>,<gamma2>)
                            <SUBSET/EXCEPT/FOR qualification>
where <p> is a variable, number, or parameter in the interval (0,1);
              <y> is a variable or a parameter (depending on what <x> is) where the computed Bi-Weibull ppf 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 = BWEPPF(3,10,0.6,4,5,2.5)
LET A = BWEPPF(P,S1,G1,L2,S2,G2)
PLOT BWEPPF(P,10,0.7,4,4,3) FOR P = 0.01 0.01 0.99

None

None

BWECDF	= Compute the Bi-Weibull cumulative distribution function.
BWECHAZ	= Compute the Bi-Weibull cumulative hazard function.
BWEHAZ	= Compute the Bi-Weibull hazard function.
BWEPDF	= Compute the Bi-Weibull probability density 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 X 
X1LABEL PROBABILITY 
TITLE BI-WEIBULL PERCENT POINT FUNCTION CR() ... 
 S1 = ^SCALE1, G1 = ^GAMMA1, LOC2 = ^LOC2, S2 = ^SCALE2, G2 = ^GAMMA2 
PLOT BWEPPF(P,SCALE1,GAMMA1,LOC2,SCALE2,GAMMA2) FOR P = 0.01 0.01 0.99