bssn (version 1.0)

reliabilitybssn: 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 \(\alpha\).

beta

scale parameter \(\beta\).

lambda

skewness parameter \(\lambda\).

Value

Rbssn gives the reliability function, Fbssn gives the failure rate or hazard function.

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

# NOT RUN {
## 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)

# }