Package 'serieslcb'

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-$\alpha$)% lower confidence bound.
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-$\alpha$)% lower confidence bound.
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-$\alpha$)% lower confidence bound.
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-$\alpha$)% lower confidence bound.
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-$\alpha$)% lower confidence bound.
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-$\alpha$)% lower confidence bound.
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-$\alpha$)% lower confidence bound.
...	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 $\alpha$-th quantile. The default value is 1000.
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-$\alpha$)% lower confidence bound.
...	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-$\alpha$)% lower confidence bound.
...	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-$\alpha$)% lower confidence bound.
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-$\alpha$)% lower confidence bound.

---

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-$\alpha$)% lower confidence bound.
...	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-$\alpha$)% lower confidence bound.

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 $\beta$.
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-$\alpha$)% lower confidence bound.
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-$\alpha$)% lower confidence bound.
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-$\alpha$)% lower confidence bound.
...	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-$\alpha$)% lower confidence bound.
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-$\alpha$)% lower confidence bound.
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.

---