phi.mult.ref.cm {AdvBinomApps}

Downscaling of failures tackled by countermeasures to greatest common chip size

Description

Function to scale failures tackled by countermeasures in burn-in studies of differently sized reference products down to the greatest common chip size of the products and to merge the downscaled information.

Usage

phi.mult.ref.cm(k, n, A.ref, K, theta, prec = 2, tailcut = 1e-08)

Arguments

k

vector of total numbers of failures for each reference product.

n

vector of numbers of inspected devices for each reference product.

A.ref

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

K

matrix with entries K[j,i] denoting the number of failures of the j-th reference product 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 reference product, 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.

prec

precision for greatest common divisor is 10^-prec (default: 2).

tailcut

probabilities for scaled failures smaller than tailcut are set to zero for each reference product (default: 1e-08). Too small values for tailcut might cause increased computation times.

Value

phi.cm

data frame with possible number of failures k.gcd (after the implementation of countermeasures) and probabilities phi.cm(k.gcd). Only failure numbers k.gcd with phi.cm(k.gcd)>0 are printed out.

A.gcd

greatest common divisor of the sizes of the reference products.

Author(s)

Daniel Kurz, Horst Lewitschnig

Maintainer: Horst Lewitschnig [e-mail]

References

D. Kurz, H. Lewitschnig and J. Pilz: Failure Probability Estimation with Differently Sized Reference Products for Semiconductor Burn-in Studies. Applied Stochastic Models in Business and Industry, 31(5): 732-744, 2015. DOI: 10.1002/asmb.2100.

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.mult.ref ci.mult.ref ci.mult.ref.cm

Examples

k<-c(1,2)
n<-c(10,10)
K<-matrix(c(1,0,1,1),2,2,byrow=TRUE)
theta<-c(0.7,0.8)
A.ref<-c(1,2)
phi.mult.ref.cm(k,n,A.ref,K,theta)

k<-c(1,2)
n<-c(110000,220000)
K<-matrix(c(1,0,0,1),2,2,byrow=TRUE) #no CM for one fail!
theta<-c(0.7,0.8)
A.ref<-c(2,3)
phi.mult.ref.cm(k,n,A.ref,K,theta)