AdvBinomApps (version 1.0)

ci.syn.cm: Upper Clopper-Pearson confidence limits under chip synergies and countermeasures

Description

Function to compute upper Clopper-Pearson confidence limits of failure probabilities on the basis of burn-in studies with countermeasures for each subset of a chip. Optionally, the required number of additional inspections for reaching a predefined target failure probability with countermeasures is returned.

Usage

ci.syn.cm(k, n, K, theta, alpha = 0.1, p.target = 1, tol = 1e-10)

Arguments

k

vector of numbers of failures for each subset.

n

vector of numbers of inspections for each subset.

K

matrix with entries K[j,i] denoting the number of failures in the j-th subset tackled with the i-th countermeasure. If two or more countermeasures have the same efficiency, they can be handled as one countermeasure for several failures. If the i-th countermeasure does not apply to the j-th subset, then set K[j,i]=0. If there is no countermeasure for a failure at all, then it does not need to be considered in K (the failure itself is already considered in k).

theta

vector of (different) effectivenesses of countermeasures.

alpha

alpha-level (1-alpha confidence level, default: 0.1).

p.target

target failure probability (optional).

tol

tolerance of uniroot-function used for computing p.hat.cm (default: 1e-10).

Value

p.hat.cm

upper Clopper-Pearson confidence limit of the failure probability of the assembled devices with countermeasures.

n.add.cm

required number of additional inspections of each subset for reaching p.target with countermeasures.

References

D. Kurz, H. Lewitschnig and J. Pilz: Failure probability estimation under additional subsystem information with application to semiconductor burn-in. Resubmitted to: Journal of Applied Statistics, 2015.

D. Kurz, H. Lewitschnig and J. Pilz: Decision-Theoretical Model for Failures Tackled by Countermeasures. IEEE Transactions on Reliability, 63(2): 583-592, 2014. DOI: 10.1109/TR.2014.2315952.

See Also

phi.syn ci.syn phi.syn.cm

Examples

#Subset 1: no failures.
#Subset 2: 1 failure - failure tackled with 80% efficiency.
k<-c(0,1)
K<-matrix(c(0,1),2,1,byrow=TRUE)
theta<-0.8
n<-c(110000,330000)
ci.syn.cm(k,n,K,theta,0.1,20e-06)

#Subset 1: 1 failure - failure tackled with 80% efficiency.
#Subset 2: 1 failure - failure tackled with 70% efficiency.
#Subset 3: 2 failures - 1 failure tackled with 80%, 
#1 failure with 70% efficiency.
k<-c(1,1,2)
K<-matrix(c(1,0,0,1,1,1),3,2,byrow=TRUE)
theta<-c(0.8,0.7)
n<-c(110000,150000,220000)
ci.syn.cm(k,n,K,theta,0.1,20e-06)

#Subset 1: 1 failure - failure tackled with 80% efficiency.
#Subset 2: 1 failure - failure without countermeasure.
#Subset 3: 2 failures - 1 failure tackled with 70% efficiency, 
#1 failure without countermeasure.
k<-c(1,1,2)
K<-matrix(c(1,0,0,0,0,1),3,2,byrow=TRUE)
theta<-c(0.8,0.7)
n<-c(110000,150000,220000)
ci.syn.cm(k,n,K,theta,0.1,20e-06)