Description Usage Arguments Value Author(s) References See Also Examples

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*.

1 2 |

`ti` |
dataset. |

`alpha` |
shape parameter |

`beta` |
scale parameter |

`lambda` |
skewness parameter |

`Rbssn`

gives the reliability function, `Fbssn`

gives the failure rate or hazard function.

Rocio Maehara [email protected] and Luis Benites [email protected]

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`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 | ```
## 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)
``` |

bssn documentation built on May 29, 2017, 2:16 p.m.

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