reliaR (version 0.01)

ExpoWeibullsurvival: Survival related functions for the Exponentiated Weibull(EW) distribution

Description

Conditional reliability function (crf), hazard function, hazard rate average (HRA) and survival function for the Exponentiated Weibull(EW) distribution with shape parameters alpha and theta.

Usage

crf.expo.weibull(x, t = 0, alpha, theta)
hexpo.weibull(x, alpha, theta)
hra.expo.weibull(x, alpha, theta)
sexpo.weibull(x, alpha, theta)

Arguments

x

vector of quantiles.

alpha

shape parameter.

theta

shape parameter.

t

age component.

Value

crf.expo.weibull gives the conditional reliability function (crf), hexpo.weibull gives the hazard function, hra.expo.weibull gives the hazard rate average (HRA) function, and sexpo.weibull gives the survival function for the Exponentiated Weibull(EW) distribution.

References

Mudholkar, G.S. and Srivastava, D.K. (1993). Exponentiated Weibull family for analyzing bathtub failure-rate data, IEEE Transactions on Reliability, 42(2), 299-302.

Murthy, D.N.P., Xie, M. and Jiang, R. (2003). Weibull Models, Wiley, New York.

Nassar, M.M., and Eissa, F. H. (2003). On the Exponentiated Weibull Distribution, Communications in Statistics - Theory and Methods, 32(7), 1317-1336.

See Also

dexpo.weibull for other Exponentiated Weibull(EW) distribution related functions;

Examples

## load data set
data(stress)
## Maximum Likelihood(ML) Estimates of alpha & theta for the data(stress)
## Estimates of alpha & theta using 'maxLik' package
## alpha.est =1.026465, theta.est = 7.824943

## Reliability indicators for data(stress):

## Reliability function
sexpo.weibull(stress, 1.026465, 7.824943)

## Hazard function
hexpo.weibull(stress, 1.026465, 7.824943)

## hazard rate average(hra)
hra.expo.weibull(stress, 1.026465, 7.824943)

## Conditional reliability function (age component=0)
crf.expo.weibull(stress, 0.00, 1.026465, 7.824943)

## Conditional reliability function (age component=3.0)
crf.expo.weibull(stress, 3.0, 1.026465, 7.824943)