| Type: | Package |
| Title: | Lower Confidence Bounds for Binomial Series System |
| Version: | 0.4.0 |
| Author: | Edward Schuberg |
| Maintainer: | Edward Schuberg <eschu003@ucr.edu> |
| Description: | Calculate and compare lower confidence bounds for binomial series system reliability. The R 'shiny' application, launched by the function launch_app(), weaves together a workflow of customized simulations and delta coverage calculations to output recommended lower confidence bound methods. |
| Depends: | R (≥ 3.3.0), shiny |
| Imports: | gplots, stats |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| LazyData: | true |
| RoxygenNote: | 6.0.1 |
| NeedsCompilation: | no |
| Packaged: | 2019-07-09 00:34:06 UTC; ed |
| Repository: | CRAN |
| Date/Publication: | 2019-07-09 04:50:10 UTC |
Bayesian method
Description
Calculate a binomial series lower confidence bound using Bayes' method with a Beta prior distribution.
Usage
bayes(s, n, alpha, MonteCarlo, beta.a, beta.b, ...)
Arguments
s |
Vector of successes. |
n |
Vector of sample sizes. |
alpha |
The significance level; to calculate a 100(1- |
MonteCarlo |
Number of samples to draw from the posterior distribution for the Monte Carlo estimate. |
beta.a |
Shape1 parameter for the Beta prior distribution. |
beta.b |
Shape2 parameter for the Beta prior distribution. |
... |
Additional arguments to be ignored. |
Value
The 100(1-\alpha)% lower confidence bound.
Examples
bayes(s=c(35, 97, 59), n=c(35, 100, 60), alpha=.10, MonteCarlo=1000, beta.a=1, beta.b=1)
Bayesian method (Jeffrey's prior)
Description
Calculate a binomial series lower confidence bound using Bayes' method with Jeffrey's prior.
Usage
bayes_jeffreys(s, n, alpha, MonteCarlo, ...)
Arguments
s |
Vector of successes. |
n |
Vector of sample sizes. |
alpha |
The significance level; to calculate a 100(1- |
MonteCarlo |
Number of samples to draw from the posterior distribution for the Monte Carlo estimate. |
... |
Additional arguments to be ignored. |
Value
The 100(1-\alpha)% lower confidence bound.
Examples
bayes_jeffreys(s=c(35, 97, 59), n=c(35, 100, 60), alpha=.10, MonteCarlo=1000)
Bayesian method (Negative Log Gamma Prior)
Description
Caclulate a binomal series lower confidence bound using Bayes' method with negative log gamma priors on the components, defined such that the prior on the system is a uniform distribution.
Usage
bayes_nlg(s, n, alpha, MonteCarlo, ...)
Arguments
s |
Vector of successes. |
n |
Vector of sample sizes. |
alpha |
The significance level; to calculate a 100(1- |
MonteCarlo |
Number of samples to draw from the posterior distribution for the Monte Carlo estimate. |
... |
Additional arguments to be ignored. |
Value
The 100(1-\alpha)% lower confidence bound.
Examples
bayes_nlg(s=c(35, 97, 59), n=c(35, 100, 60), alpha=.10, MonteCarlo=1000)
Bayesian method (Uniform prior)
Description
Calculate a binomial series lower confidence bound using Bayes' method with a uniform prior distribution.
Usage
bayes_uniform(s, n, alpha, MonteCarlo, ...)
Arguments
s |
Vector of successes. |
n |
Vector of sample sizes. |
alpha |
The significance level; to calculate a 100(1- |
MonteCarlo |
Number of samples to draw from the posterior distribution for the Monte Carlo estimate. |
... |
Additional arguments to be ignored. |
Value
The 100(1-\alpha)% lower confidence bound.
Examples
bayes_uniform(s=c(35, 97, 59), n=c(35, 100, 60), alpha=.10, MonteCarlo=1000)
Chao-Huwang method
Description
Calculate a binomial series lower confidence bound using Chao and Huwang's (1987) method.
Usage
chao_huwang(s, n, alpha, MonteCarlo, ...)
Arguments
s |
Vector of successes. |
n |
Vector of sample sizes. |
alpha |
The significance level; to calculate a 100(1- |
MonteCarlo |
Number of samples to draw from the posterior distribution for the Monte Carlo estimate. |
... |
Additional arguments to be ignored. |
Value
The 100(1-\alpha)% lower confidence bound.
Examples
chao_huwang(s=c(35, 97, 59), n=c(35, 100, 60), alpha=.10, MonteCarlo=1000)
Coit's method
Description
Calculate a binomial series lower confidence bound using Coit's (1997) method.
Usage
coit(s, n, alpha, use.backup = FALSE, backup.method, ...)
Arguments
s |
Vector of successes. |
n |
Vector of sample sizes. |
alpha |
The significance level; to calculate a 100(1- |
use.backup |
If TRUE, then a backup.method in the will be used for the methods with calculate LCB = 1 in the case of no failures across all components. If FALSE (default), no backup.method is used. |
backup.method |
The backup method which is used for the methods which calculate LCB = 1 in the case of zero failures. Use function name. |
... |
Additional arguments to be ignored. |
Value
The 100(1-\alpha)% lower confidence bound.
Examples
coit(s=c(35, 97, 59), n=c(35, 100, 60), alpha=.10)
Easterling's method
Description
Calculate a binomial series lower confidence bound using Easterling's (1972) method.
Usage
easterling(s, n, alpha, ...)
Arguments
s |
Vector of successes. |
n |
Vector of sample sizes. |
alpha |
The significance level; to calculate a 100(1- |
... |
Additional arguments to be ignored. |
Value
The 100(1-\alpha)% lower confidence bound.
Examples
easterling(s=c(35, 97, 59), n=c(35, 100, 60), alpha=.10)
Launch Shiny App
Description
Launches an instance of an R Shiny App, which runs locally on the user's computer.
Usage
launch_app(MonteCarlo = 1000, use.backup = TRUE,
backup.method = lindstrom_madden_AC, sample.omega = "corners",
number = 50)
Arguments
MonteCarlo |
The number of Monte Carlo samples to take. E.g. In a Bayesian method, how many samples to take from a posterior distribution to estimate the lower |
use.backup |
If TRUE (default), then a backup.method in the will be used for the methods with calculate LCB = 1 in the case of no failures across all components. If FALSE, no backup.method is used. |
backup.method |
The backup method which is used for the methods which calculate LCB = 1 in the case of zero failures. The default is lindstrom_madden_AC. |
sample.omega |
The method used to define component reliabilities. Can be only one of "corners" (default), "random", or "both". See Details below. |
number |
The number of component reliability vectors sampled if sample.omega = "random" or "both". Default is 50. |
Details
If the "Download Histograms" button does not work, it can be fixed by launching the Shiny App on your local browser. This can be done by clicking on "Open in Browser" located at the top of your Shiny App. This seems to be an issue with the Download Handler that Shiny uses.
Define
\Omega = \{(p_1, p_2, \dots , p_m): \prod_{i=1}^m p_i \in [ R_L , R_U ] \}
and
\Omega ' = \{(p_1, p_2, \dots , p_m): p_i = R_L^{1/m} { or } R_U^{1/m} \forall i \}
. If sample.omega = "corners" (the default), then the elements of
\Omega '
are used for component reliabilities, of which there are
2^m
combinations. If sample.omega = "random", then each component reliability is sampled uniformly from the interval
[ R_L^m , R_U^m ]
. If sample.omega = "both", then the results of "corners" and "random" are appended together and both are used.
Lindstrom and Madden's method
Description
Calculate a binomial series lower confidence bound using Lindstrom and Madden's (1962) method.
Usage
lindstrom_madden(s, n, alpha, ...)
Arguments
s |
Vector of successes. |
n |
Vector of sample sizes. |
alpha |
The significance level; to calculate a 100(1- |
... |
Additional arguments to be ignored. |
Value
The 100(1-\alpha)% lower confidence bound.
Examples
lindstrom_madden(s=c(35, 97, 59), n=c(35, 100, 60), alpha=.10)
Lindstrom and Madden's method with Agresti-Coull
Description
Calculate a binomial series lower confidence bound using Agresti-Coull (1998) lower confidence bound calculation in the Lindstrom and Madden's (1962) method.
Usage
lindstrom_madden_AC(s, n, alpha, ...)
Arguments
s |
Vector of successes. |
n |
Vector of sample sizes. |
alpha |
The significance level; to calculate a 100(1- |
... |
Additional arguments to be ignored. |
Value
The 100(1-\alpha)% lower confidence bound.
Examples
lindstrom_madden_AC(s=c(35, 97, 59), n=c(35, 100, 60), alpha=.10)
Madansky's method
Description
Calculate a binomial series lower confidence bound using Madansky's (1965) method.
Usage
madansky(s, n, alpha, use.backup = FALSE, backup.method, ...)
Arguments
s |
Vector of successes. |
n |
Vector of sample sizes. |
alpha |
The significance level; to calculate a 100(1- |
use.backup |
If TRUE, then a backup.method in the will be used for the methods with calculate LCB = 1 in the case of no failures across all components. If FALSE (default), no backup.method is used. |
backup.method |
The backup method which is used for the methods which calculate LCB = 1 in the case of zero failures. Use function name. |
... |
Additional arguments to be ignored. |
Value
The 100(1-\alpha)% lower confidence bound. Note that if there are zero observed
failures across all components, the output is LCB = 0.
Examples
madansky(s=c(35, 97, 59), n=c(35, 100, 60), alpha=.10)
Lagrange multiplier in Madansky's method
Description
This function is called in the madansky() function to solve for the Lagrange multipliers.
Usage
madansky.fun(lam, s, n, alpha)
Arguments
lam |
The value of the Lagrange multiplier |
s |
Vector of successes. |
n |
Vector of sample sizes. |
alpha |
The significance level; to calculate a 100(1- |
Mann and Grubb's method
Description
Calculate a binomial series lower confidence bound using Mann and Grubb's (1974) method.
Usage
mann_grubbs(s, n, alpha, ...)
Arguments
s |
Vector of successes. |
n |
Vector of sample sizes. |
alpha |
The significance level; to calculate a 100(1- |
... |
Additional arguments to be ignored. |
Value
The 100(1-\alpha)% lower confidence bound.
Examples
mann_grubbs(s=c(35, 97, 59), n=c(35, 100, 60), alpha=.10)
Function to calculate the LCB in the Mann-Grubbs method.
Description
Calculate the LCB in the Mann-Grubbs method.
Usage
mann_grubbs_calc(s, n, A, alpha)
Arguments
s |
Vector of successes. |
n |
Vector of sample sizes. |
A |
The restricted sum, as caclulated by the mann_grubbs_sum() function. |
alpha |
The significance level; to calculate a 100(1- |
Value
The LCB for the Mann-Grubbs method.
Function to calculate the restricted sum in the Mann-Grubbs method.
Description
Calculate the restricted sum in the Mann-Grubbs method.
Usage
mann_grubbs_sum(s, n)
Arguments
s |
Vector of successes. |
n |
Vector of sample sizes. |
Value
The restricted sum.
Function of \beta in the Myhre-Rennie 2 method
Description
This function is called in myhre_rennie2() function to solve for the \beta value.
Usage
mr.fun(beta, s, n)
Arguments
beta |
The value of |
s |
Vector of successes. |
n |
Vector of sample sizes. |
Myhre and Rennie (modified ML) method
Description
Calculate a binomial series lower confidence bound using the Myhre-Rennie (modified ML) method (1986).
Usage
myhre_rennie1(s, n, alpha, use.backup = FALSE, backup.method, ...)
Arguments
s |
Vector of successes. |
n |
Vector of sample sizes. |
alpha |
The significance level; to calculate a 100(1- |
use.backup |
If TRUE, then a backup.method in the will be used for the methods with calculate LCB = 1 in the case of no failures across all components. If FALSE (default), no backup.method is used. |
backup.method |
The backup method which is used for the methods which calculate LCB = 1 in the case of zero failures. Use function name. |
... |
Additional arguments to be ignored. |
Value
The 100(1-\alpha)% lower confidence bound.
Examples
myhre_rennie1(s=c(35, 97, 59), n=c(35, 100, 60), alpha=.10)
Myhre and Rennie (reliability invariant) method
Description
Calculate a binomial series lower confidence bound using the Myhre-Rennie (reliability invariant) method (1986).
Usage
myhre_rennie2(s, n, alpha, use.backup = FALSE, backup.method, ...)
Arguments
s |
Vector of successes. |
n |
Vector of sample sizes. |
alpha |
The significance level; to calculate a 100(1- |
use.backup |
If TRUE, then a backup.method in the will be used for the methods with calculate LCB = 1 in the case of no failures across all components. If FALSE (default), no backup.method is used. |
backup.method |
The backup method which is used for the methods which calculate LCB = 1 in the case of zero failures. Use function name. |
... |
Additional arguments to be ignored. |
Value
The 100(1-\alpha)% lower confidence bound.
Examples
myhre_rennie2(s=c(35, 97, 59), n=c(35, 100, 60), alpha=.10)
Nishime's method
Description
Calculate a binomial series lower confidence bound using Nishime's (1959) method.
Usage
nishime(s, n, alpha, ...)
Arguments
s |
Vector of successes. |
n |
Vector of sample sizes. |
alpha |
The significance level; to calculate a 100(1- |
... |
Additional arguments to be ignored. |
Value
The 100(1-\alpha)% lower confidence bound.
Examples
nishime(s=c(35, 97, 59), n=c(35, 100, 60), alpha=.10)
Sampling from Posterior of Negative Log Gamma prior and Binomial data.
Description
Randomly sample from the posterior distribution resulting from a NLG prior and Binomial data.
Usage
nlg.post.sample(sample.size, shape, scale, s, n)
Arguments
sample.size |
The number of draws from the posterior distribution. |
shape |
The shape parameter for the NLG prior. |
scale |
The scale parameter for the NLG prior. |
s |
The number of successes for the binomial data (should be a scalar). |
n |
The number of tests for the binomial data (should be a scalar). |
Examples
nlg.post.sample(sample.size=50, shape=.2, scale=1, s=29, n=30)
Normal approximation method
Description
Calculate a binomial series lower confidence bound using a normal approximation with MLE estimates.
Usage
normal_approximation(s, n, alpha, use.backup = FALSE, backup.method, ...)
Arguments
s |
Vector of successes. |
n |
Vector of sample sizes. |
alpha |
The significance level; to calculate a 100(1- |
use.backup |
If TRUE, then a backup.method in the will be used for the methods with calculate LCB = 1 in the case of no failures across all components. If FALSE (default), no backup.method is used. |
backup.method |
The backup method which is used for the methods which calculate LCB = 1 in the case of zero failures. Use function name. |
... |
Additional arguments to be ignored. |
Value
The 100(1-\alpha)% lower confidence bound.
Examples
normal_approximation(s=c(35, 97, 59), n=c(35, 100, 60), alpha=.10)
Matrix of p-vector combinations
Description
Calculate a matrix of p-vector combinations (component reliabilities) which lie in the specified interval of system reliability. Rows correspond to p-vectors and columns correspond to components.
Usage
pm(Rs.int, m)
Arguments
Rs.int |
Interval (or single number) of total system reliability. |
m |
Number of components. |
Details
Denote Rs.int = (R_L, R_U). This function calculates all elements of the set
\Omega ' = \{(p_1, p_2, \dots , p_m): p_i = R_L^{1/m} { or } R_U^{1/m} \forall i \}
.
Value
The 2^m by m matrix of p-vector combinations.
Examples
pm(Rs.int = c(.9, .95), m=3)
Matrix of p-vector combinations sampled randomly.
Description
Randomly sample to build a matrix of p-vector combinations (component reliabilities) which lie in the specified interval of system reliability. Rows correspond to p-vectors and columns correspond to components.
Usage
pm.random(Rs.int, m, number)
Arguments
Rs.int |
Interval (or single number) of total system reliability. |
m |
Number of components. |
number |
The number of random samples to draw. |
Examples
pm.random(Rs.int=c(.9, .95), m=3, number=100)
Rice and Moore's method
Description
Calculate a binomial series lower confidence bound using Rice and Moore's (1983) method.
Usage
rice_moore(s, n, alpha, MonteCarlo, f.star = 1.5 - min(n) + 0.5 * sqrt((3 - 2
* min(n))^2 - 4 * (min(n) - 1) * log(alpha) * qchisq(p = alpha, df = 2)), ...)
Arguments
s |
Vector of successes. |
n |
Vector of sample sizes. |
alpha |
The significance level; to calculate a 100(1- |
MonteCarlo |
Number of samples to draw from the posterior distribution for the Monte Carlo estimate. |
f.star |
The number of psuedo-failures to use for a component that exhibits zero observed failures. The default value is from the log-gamma procedure proposed by Gatliffe (1976), and is the value used by Rice and Moore. |
... |
Additional arguments to be ignored. |
Value
The 100(1-\alpha)% lower confidence bound.
Examples
rice_moore(s=c(35, 97, 59), n=c(35, 100, 60), alpha=.10, MonteCarlo=1000)
Root Mean Square Error
Description
Calculate the root mean squared errors of the LCB's from the true system reliability. A measure of spread.
Usage
rmse.LCB(LCB, R)
Arguments
LCB |
Vector of LCB's. |
R |
The true system reliability . |
Value
The root mean squared error of the LCB's from the true system reliability.