reliabilitybssn {bssn} | R Documentation |
Reliability Function for the Birnbaum-Saunders model based on Skew-Normal distribution
Description
Two useful descriptors in reliability analysis are the reliability function (rf), and the failure rate (fr) function or hazard function. For a non-negative random variable t
with pdf f(t)
(and cdf F(t)
), its distribution can be characterized equally in terms of the rf, or of the fr, which are respectively defined by R(t)=1-F(t)
, and h(t)=f(t)/R(t)
, for t>0
,and 0<R(t)<1
.
Usage
Rebssn(ti,alpha=0.5,beta=1,lambda=1.5)
Fbssn(ti,alpha=0.5,beta=1,lambda=1.5)
Arguments
ti |
dataset. |
alpha |
shape parameter |
beta |
scale parameter |
lambda |
skewness parameter |
Value
Rbssn
gives the reliability function, Fbssn
gives the failure rate or hazard function.
Author(s)
Rocio Maehara rmaeharaa@gmail.com and Luis Benites lbenitesanchez@gmail.com
References
Leiva, V., Vilca-Labra, F. E., Balakrishnan, N. e Sanhueza, A. (2008). A skewed sinh-normal distribution and its properties and application to air pollution. Comm. Stat. Theoret. Methods. Submetido.
Guiraud, P., Leiva, V., Fierro, R. (2009). A non-central version of the Birnbaum-Saunders distribution for reliability analysis. IEEE Transactions on Reliability 58, 152-160.
See Also
bssn
, EMbssn
, momentsbssn
, ozone
, Rebssn
Examples
## Let's compute some realiability functions for a Birnbaum-Saunders model based on
## Skew normal Distribution for different values of the shape parameter.
ti <- seq(0,2,0.01)
f1 <- Rebssn(ti,0.75,1,1)
f2 <- Rebssn(ti,1,1,1)
f3 <- Rebssn(ti,1.5,1,1)
f4 <- Rebssn(ti,2,1,1)
den <- cbind(f1,f2,f3,f4)
matplot(ti,den,type="l", col=c("deepskyblue4","firebrick1","darkmagenta","aquamarine4"),
ylab="S(t)", xlab="t",lwd=2)
legend(1.5,1,c(expression(alpha==0.75), expression(alpha==1), expression(alpha==1.5),
expression(alpha==2)),col= c("deepskyblue4","firebrick1","darkmagenta","aquamarine4"),
lty=1:4,lwd=2,seg.len=2,cex=0.9,box.lty=0,bg=NULL)
## Let's compute some hazard functions for a Birnbaum Saunders model based on
## Skew normal Distribution for different values of the skewness parameter.
ti <- seq(0,2,0.01)
f1 <- Fbssn(ti,0.5,1,-1)
f2 <- Fbssn(ti,0.5,1,-2)
f3 <- Fbssn(ti,0.5,1,-3)
f4 <- Fbssn(ti,0.5,1,-4)
den <- cbind(f1,f2,f3,f4)
matplot(ti,den,type = "l", col = c("deepskyblue4","firebrick1", "darkmagenta", "aquamarine4"),
ylab = "h(t)" , xlab="t",lwd=2)
legend(0.1,23, c(expression(lambda==-1), expression(lambda==-2), expression(lambda == -3),
expression(lambda == -4)), col = c("deepskyblue4", "firebrick1", "darkmagenta","aquamarine4"),
lty=1:4,lwd=2,seg.len=2,cex=0.9,box.lty=1,bg=NULL)