WEICHAZ

WEICHAZ (LET)

Library Function

Compute the Weibull cumulative hazard function with tail length parameter .

For the minimum order statistic, the standard form of the Weibull cumulative hazard function is:

For the maximum order statistic, the standard form of the Weibull hazard function is:

LET <y> = WEICHAZ(<x>,<gamma>,<loc>, <scale>)
                        <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 Weibull cumulative hazard value is stored;
              <gamma> is a positive number, parameter, or variable that specifies the tail length parameter;
              <loc> is a positive number, parameter, or variable that specifies the location parameter;
              <scale> is a positive number, parameter, or variable that specifies the scale parameter;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

The location and scale parameters are optional.

LET A = WEICHAZ(3,2)
LET Y = WEICHAZ(X,4)
LET Y = WEICHAZ(X,2,0,5)
PLOT WEICHAZ(X,2) FOR X = 0.01 0.01 10

The SET MINMAX command specifies whether the minimum or maximum order statistic form is used. Entering SET MINMAX 2 specifies the maximum order statistic while entering SET MINMAX specifies the minimum order statistic.

For the minimum order statistic, the general form of the Weibull hazard function is:

For the maximum order statistic, the general form of the Weibull probability density function is:

where is the location parameter and is the scale parameter.

None

None

WEIHAZ	= Compute the Weibull hazard function.
WEICDF	= Compute the Weibull cumulative distribution function.
WEIPDF	= Compute the Weibull probability density function.
WEIPPF	= Compute the Weibull percent point function.
EXPHAZ	= Compute the exponential cumulative hazard function.
EV1HAZ	= Compute the extreme value type I hazard function.
EV2HAZ	= Compute the extreme value type II hazard function.
LGNHAZ	= Compute the lognormal hazard function.

"Continuous Univariate Distributions--Vol. I", 2nd. Ed., Johnson, Kotz, and Balakrishnan, John Wiley and Sons, 1994.

"Statistical Distributions", 2nd. Edition, Evans, Hastings, and Peacock, Wiley and Sons, 1993 (chapter 18).

Reliability Analysis

1998/5

MULTIPLOT 2 2
MULTIPLOT CORNER COORDINATES 0 0 100 100
SET MINMAX 1
X1LABEL GAMMA = 1
PLOT WEICHAZ(X,1) FOR X = 0.01 0.01 3
X1LABEL GAMMA = 2
PLOT WEICHAZ(X,2) FOR X = 0.01 0.01 3
X1LABEL GAMMA = 5
PLOT WEICHAZ(X,5) FOR X = 0.01 0.01 3
X1LABEL GAMMA = 0.5
PLOT WEICHAZ(X,0.5) FOR X = 0.01 0.01 3
END OF MULTIPLOT
MOVE 50 97
JUSTIFICATION CENTER
TEXT WEIBULL HAZARD PLOTS