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 α. `beta` scale parameter β. `lambda` skewness parameter λ.

### 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.

`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)

```

[Package bssn version 1.0 Index]