AdvBinomApps (version 1.0)

ci.sas: Separate area scaling for upper Clopper-Pearson confidence limits

Description

Function to compute upper Clopper-Pearson confidence limits of failure probabilities of follower products by means of separate area scaling (SAS). Furthermore, the validity of the SAS in comparison to the classical area scaling (CAS) is evaluated. Optionally, the required numbers of additional inspections of the reference product in order to reach the predefined target failure probability of the follower product according to the CAS and SAS are returned.

Usage

ci.sas(k, n, A.ref, A.follow, alpha = 0.1, p.target = 1, atol = 1e-08)

Arguments

k

vector of numbers of failures for each subset on reference product (total number of failures on reference product = sum of entries of k).

n

number of inspected devices in burn-in study of reference product.

A.ref

vector of sizes for each subset on reference product (in mm^2).

A.follow

vector of sizes for each subset on follower product (in mm^2).

alpha

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

p.target

target failure probability of follower product (optional).

atol

tolerance of multiroot-function used for computing p.sas (default: 1e-08). For further details, see description of multiroot-function.

Value

p.cas

vector of upper Clopper-Pearson confidence limits of failure probabilities for each subset on reference product according to CAS.

p.sas

vector of upper Clopper-Pearson confidence limits of failure probabilities for each subset on reference product according to SAS.

p.follow.cas

upper Clopper-Pearson confidence limit of the failure probability of the follower product according to CAS.

p.follow.sas

upper Clopper-Pearson confidence limit of the failure probability of the follower product according to SAS.

delta

evidence factor against CAS.

n.add.cas

required number of additional inspections of the reference product in order to reach p.target of the follower product according to CAS.

n.add.sas

required number of additional inspections of the reference product in order to reach p.target of the follower product according to SAS.

Details

Function makes use of multiroot-function of the package rootSolve to solve non-linear equation system for the subset failure probabilities.

Appropriate starting values for multiroot are chosen automatically.

In case of non-convergence of multiroot-function, NA is returned.

Function designed and verified for number of subsets < 6.

References

D. Kurz, H. Lewitschnig and J. Pilz: An Advanced Area Scaling Approach for Semiconductor Burn-in. Microelectronics Reliability, 55(1): 129-137, 2015. DOI: 10.1016/j.microrel.2014.09.007.

See Also

ci.sas.cm

Examples

k<-c(1,0)
n<-100000
A.ref<-c(1,1.5)
A.follow<-c(1,2)
p.target<-20e-06
ci.sas(k,n,A.ref,A.follow,0.1,p.target)

k<-c(2,1,0)
n<-100000
A.ref<-c(2,3,4)
A.follow<-c(1,2,3)
p.target<-20e-06
ci.sas(k,n,A.ref,A.follow,0.1,p.target)

k<-c(1,1,0,2)
n<-100000
A.ref<-c(1,1,1,1)
A.follow<-c(3,4,5,6)
p.target<-20e-06
ci.sas(k,n,A.ref,A.follow,0.1,p.target)