Required Sample Size - Countermeasure Model

Description

Provides the required sample size with respect to the extended upper Clopper-Pearson limit for a failure model, where countermeasures are introduced.

Usage

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cm.n.clopper.pearson(p, size, cm.effect, alpha = 0.1, uniroot.lower = k + 1,
  uniroot.upper = 1e+100, uniroot.tol = 1e-10, uniroot.maxiter = 1e+05)

Arguments

p

target probability.

size

vector of the number of failures for each type.

cm.effect

vector of the success probabilities to solve a failure for each type. Corresponds to the probabilities pi of a generalized binomial distribution.

alpha

significance level for the (1-alpha)* 100% confidence level (default alpha=0.1).

uniroot.lower

The value of the lower parameter sent to uniroot. Lower bound of the interval to be searched. See uniroot for more details.

uniroot.upper

The value of the upper parameter sent to uniroot. Upper bound of the interval to be searched. See uniroot for more details.

uniroot.maxiter

The value of the maxiter parameter sent to uniroot. Maximum number of iterations. See uniroot for more details.

uniroot.tol

The value of the tol parameter sent to uniroot. Convergence tolerance. See uniroot for more details.

Details

Provides the required sample size with respect to the extended upper Clopper-Pearson limit. It applies for the case that failures are tackled by countermeasures. That means countermeasures with different effectivities for each failure type are introduced. See the references for further information.

Value

The value for the required sample size.

References

D.Kurz, H.Lewitschnig, J.Pilz, Decision-Theoretical Model for Failures which are Tackled by Countermeasures, IEEE Transactions on Reliability, Vol. 63, No. 2, June 2014.

See Also

uniroot,dgbinom,cm.clopper.pearson.ci,n.clopper.pearson

Examples

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## target failure probability p=0.00001, 2 failures divided in 2 failure types k1=1, k2=1.
## 2 countermeasures with effectivities p1=0.5, p2=0.8
cm.n.clopper.pearson(0.00001,size=c(1,1),cm.effect=c(0.5,0.8))
# 365299