The hardware and bandwidth for this mirror is donated by dogado GmbH, the Webhosting and Full Service-Cloud Provider. Check out our Wordpress Tutorial.
If you wish to report a bug, or if you are interested in having us mirror your free-software or open-source project, please feel free to contact us at mirror[@]dogado.de.

Type: Package
Title: Computation and Estimation of Reliability of Stress-Strength Models
Version: 1.0.2
Date: 2016-04-29
Author: Alessandro Barbiero <alessandro.barbiero@unimi.it>, Riccardo Inchingolo <dott.inchingolo_r@libero.it>
Maintainer: Alessandro Barbiero <alessandro.barbiero@unimi.it>
Description: Reliability of (normal) stress-strength models and for building two-sided or one-sided confidence intervals according to different approximate procedures.
License: GPL-2 | GPL-3 [expanded from: GPL]
LazyLoad: yes
Packaged: 2016-04-30 07:57:22 UTC; Barbiero
Repository: CRAN
Date/Publication: 2016-05-01 00:44:38
NeedsCompilation: no

Computation and Sample Estimation of Reliability of Stress-Strength Models

Description

Reliability of (normal) stress-strength models and for building two-side or one-side confidence intervals according to different approximate procedures.

Details

Package: StressStrength
Type: Package
Version: 1.0.2
Date: 2016-04-29
License: GPL
LazyLoad: yes

Author(s)

Alessandro Barbiero, Riccardo Inchingolo

Maintainer: Alessandro Barbiero <alessandro.barbiero@unimi.it>

References

Kotz S, Lumelskii Y, Pensky M (2003) The stress-strength model and its generalizations: theory and applications. World Scientific, Singapore

Guo H, Krishnamoorthy K (2004) New approximate inferential methods for the reliability parameter in a stress-strength model: The normal case. Commun Stat Theory Methods 33:1715-1731

Computation of reliability of stress-strength models

Description

For a stress-strength model, with independent r.v. X and Y representing the strength and the stress respectively, the function computes the reliability R=P(X>Y)

Usage

SSR(parx, pary, family = "normal")

Arguments

parx

parameters of X distribution (for the normal distribution, mean \mu_x and standard deviation \sigma_x)

pary

parameters of Y distribution (for the normal distribution, mean \mu_y and standard deviation \sigma_y)

family

family distribution for both X and Y (now, only "normal" available)

Details

The function computes R=P(X>Y) where X and Y are independent r.v. following the family distribution with distributional parameters parx and pary.

Value

R=P(X>Y). For normal distributions, R=\Phi(d) with d=(\mu_x-\mu_y)/\sqrt{\sigma_x^2+\sigma_y^2}.

Author(s)

Alessandro Barbiero, Riccardo Inchingolo

References

Kotz S, Lumelskii Y, Pensky M (2003) The stress-strength model and its generalizations: theory and applications. World Scientific, Singapore

See Also

estSSR

Examples

# let X be a normal r.v. with mean 1 and sd 1;
# and Y a normal r.v. with mean 0 and sd 2
# X and Y independent
parx<-c(1, 1)
pary<-c(0, 2)
# reliability of the stress-strength model (X=strength, Y=stress)
SSR(parx,pary)
# changing the parameters of Y
pary<-c(1.5, 2)
# reliability of the stress-strength model (X=strength, Y=stress)
SSR(parx,pary)

Sample estimation of reliability of stress-strength models

Description

The function provides sample estimates of reliability of stress-strength models, where stress and strength are modeled as independent r.v., whose distribution form is known except for the values of its parameters, assumed all unknown

Usage

estSSR(x, y, family="normal", twoside=TRUE, type="RG", alpha=0.05, B=2000)

Arguments

x

a random sample from r.v. X modeling strength

y

a random sample from r.v. Y modeling stress

family

the distribution of both X and Y

twoside

if TRUE, the function computes two-side confidence intervals; otherwise, one-side (a lower bound)

type

type of confidence interval (CI) to be built. For the normal family, "RG" stands for Reiser-Guttman, "AN" for large sample (asymptotically normal), "LOGIT" or "ARCSIN" for logit or arcsin variance stabilizing tranformations, "B" for percentile bootstrap, "GK" for Guo-Krishnamoorthy (one-sided only).

alpha

the complement to one of the nominal confidence level

B

number of bootstrap replicates (for type "B")

Details

For more details, please have a look at the references listed below

Value

A list comprising

ML_est

the sample value of the maximum likelihood estimator; for normal r.v. \hat{R}=\Phi[(\bar{x}-\bar{y})/\sqrt{\hat{\sigma}_x^2+\hat{\sigma}_y^2}], where \bar{x} and \bar{y} are the sample means, and \hat{\sigma}_x^2, \hat{\sigma}_y^2 the biased maximum likelihood variance estimators

Downton_est

(for normal r.v.) the sample value of one of the approximated UMVU estimators proposed by Downton \hat{R}'=\Phi[(\bar{x}-\bar{y})/\sqrt{s_x^2+s_y^2}]

CI

the confidence interval

confidence_level

the nominal confidence level 1-\alpha

Author(s)

Alessandro Barbiero, Riccardo Inchingolo

References

Barbiero A (2011) Confidence Intervals for Reliability of Stress-Strength Models in the Normal Case, Comm Stat Sim Comp 40(6):907-925

Downton F. (1973) The Estimation of Pr (Y < X) in the Normal Case, Technometrics , 15(3):551-558

Kotz S, Lumelskii Y, Pensky M (2003) The stress-strength model and its generalizations: theory and applications. World Scientific, Singapore

Guo H, Krishnamoorthy K (2004) New approximate inferential methods for the reliability parameter in a stress-strength model: The normal case. Commun Stat Theory Methods 33:1715-1731

Mukherjee SP, Maiti SS (1998) Stress-strength reliability in the Weibull case. Frontiers In Reliability 4:231-248. WorldScientific, Singapore

Reiser BJ, Guttman I (1986) Statistical inference for P(Y<X): The normal case. Technometrics 28:253-257

See Also

SSR

Examples

# distributional parameters of X and Y
parx<-c(1, 1)
pary<-c(0, 2)
# sample sizes
n<-10
m<-20
# true value of R
SSR(parx,pary)
# draw independent random samples from X and Y
x<-rnorm(n, parx[1], parx[2])
y<-rnorm(m, pary[1], pary[2])
# build two-sided confidence intervals
estSSR(x, y, type="RG")
estSSR(x, y, type="AN")
estSSR(x, y, type="LOGIT")
estSSR(x, y, type="ARCSIN")
estSSR(x, y, type="B")
estSSR(x, y, type="B",B=1000) # change number of bootstrap replicates
# and one-sided
estSSR(x, y, type="RG", twoside=FALSE)
estSSR(x, y, type="AN", twoside=FALSE)
estSSR(x, y, type="LOGIT", twoside=FALSE)
estSSR(x, y, type="ARCSIN", twoside=FALSE)
estSSR(x, y, type="B", twoside=FALSE)
estSSR(x, y, type="GK", twoside=FALSE)
# changing sample sizes
n<-20
m<-30
x<-rnorm(n, parx[1], parx[2])
y<-rnorm(m, pary[1], pary[2])
# build tow-sided confidence intervals
estSSR(x, y, type="RG")
estSSR(x, y, type="AN")
estSSR(x, y, type="LOGIT")
estSSR(x, y, type="ARCSIN")
estSSR(x, y, type="B")

Numerical solution for an equation involving noncentral T cdf

Description

It provides the solution of the equation F_t(q;df,x)=p, where F_t is the cdf (calculated in q) of a non-central Student r.v. with df degrees of freedom and unkwon noncentrality parameter x. In R code, gkf provides the solution of pt(q,df,x)=p.

Usage

gkf(p, q, df, eps = 1e-05)

Arguments

p

a probability

q

a real value

df

degrees of freedom of noncentral T

eps

tolerance

Details

This function is used for building Guo-Krishnamoorthy confidence intervals for R

Value

the noncentrality parameter x satisfying the equation F_t(q;df,x)=p

Author(s)

Alessandro Barbiero, Riccardo Inchingolo

References

Guo H, Krishnamoorthy K (2004) New approximate inferential methods for the reliability parameter in a stress-strength model: The normal case. Commun Stat Theory Methods 33:1715-1731

See Also

estSSR

Examples

p<-0.95
q<-5
df<-12
ncp<-gkf(p, q, df)
ncp
# check if the result is correct
pt(q, df, ncp)
# OK
# changing the tolerance
ncp<-gkf(p, q, df, eps=1e-10)
ncp
pt(q, df, ncp)

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.