| Title: | Upper Clopper-Pearson Confidence Limits for Burn-in Studies under Additional Available Information |
|---|---|
| Description: | Functions to compute upper Clopper-Pearson confidence limits of early life failure probabilities and required sample sizes of burn-in studies under further available information, e.g. from other products or technologies. |
| Authors: | Daniel Kurz [aut], Horst Lewitschnig [aut, cre] |
| Maintainer: | Horst Lewitschnig <[email protected]> |
| License: | GPL-3 |
| Version: | 1.0 |
| Built: | 2024-10-31 06:27:58 UTC |
| Source: | CRAN |
Functions to compute upper Clopper-Pearson confidence limits of early life failure probabilities and required sample sizes of burn-in studies under further available information, e.g. from other products or technologies.
| Package: | AdvBinomApps |
| Type: | Package |
| Version: | 1.0 |
| Date: | 2016-04-05 |
| License: | GPL-3 |
Daniel Kurz, Horst Lewitschnig
Maintainer: Horst Lewitschnig [email protected]
C.J. Clopper and E.S. Pearson: The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika, 26(4): 404-413, 1934.
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.
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: An Advanced Area Scaling Approach for Semiconductor Burn-in. Microelectronics Reliability, 55(1): 129-137, 2015. DOI: 10.1016/j.microrel.2014.09.007.
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.
Acknowledgment
The work has been performed in the project EPT300, co-funded by grants from Austria, Germany, Italy, The Netherlands and the ENIAC Joint Undertaking. This project is co-funded within the programme "Forschung, Innovation und Technologie fuer Informationstechnologie" by the Austrian Ministry for Transport, Innovation and Technology.
#MULTIPLE REFERENCE PRODUCTS: k<-c(1,2) n<-c(110000,138000) A.ref<-c(5.21,10.71) A.follow<-8.5 p.target<-20e-06 ci.mult.ref(k,n,A.ref,A.follow,p.target=p.target) #SYNERGIES k<-c(0,1) n<-c(110000,330000) ci.syn(k,n,0.1,20e-06) #SEPARATE AREA SCALING k<-c(1,0) n<-110000 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)#MULTIPLE REFERENCE PRODUCTS: k<-c(1,2) n<-c(110000,138000) A.ref<-c(5.21,10.71) A.follow<-8.5 p.target<-20e-06 ci.mult.ref(k,n,A.ref,A.follow,p.target=p.target) #SYNERGIES k<-c(0,1) n<-c(110000,330000) ci.syn(k,n,0.1,20e-06) #SEPARATE AREA SCALING k<-c(1,0) n<-110000 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)
Function to compute upper Clopper-Pearson confidence limits of failure probabilities on the basis of differently sized reference products. Optionally, the required numbers of additional inspections for each reference product to reach a predefined target failure probability of the follower product are returned.
ci.mult.ref(k, n, A.ref, A.follow, alpha = 0.1, p.target = 1, prec = 2, tailcut = 1e-08, tol = 1e-12)ci.mult.ref(k, n, A.ref, A.follow, alpha = 0.1, p.target = 1, prec = 2, tailcut = 1e-08, tol = 1e-12)
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). |
A.follow |
size of follower product. |
alpha |
alpha-level (1-alpha confidence level, default: 0.1). |
p.target |
target failure probability of follower product (optional). |
prec |
precision for greatest common divisor is 10^- |
tailcut |
probabilities for scaled failures smaller than |
tol |
tolerance of |
p.ref |
vector of upper Clopper-Pearson confidence limits for each reference product (without the other reference products). |
p.mm |
upper Clopper-Pearson confidence limit of the failure probability per mm^2 (on the basis of all reference products). |
p.follow |
upper Clopper-Pearson confidence limit of the failure probability of the follower product (on the basis of all reference products). |
n.add |
vector of required numbers of additional inspections for each reference product in order to reach p.target for the follower product. |
Daniel Kurz, Horst Lewitschnig
Maintainer: Horst Lewitschnig [email protected]
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.
phi.mult.ref
ci.mult.ref.cm
phi.mult.ref.cm
k<-c(1,2) n<-c(110000,138000) A.ref<-c(5.21,10.71) A.follow<-8.5 p.target<-20e-06 ci.mult.ref(k,n,A.ref,A.follow,p.target=p.target) k<-c(1,2,2) n<-c(110000,138000,170000) A.ref<-c(5.21,10.71,7.89) A.follow<-8.5 p.target<-20e-06 ci.mult.ref(k,n,A.ref,A.follow,p.target=p.target)k<-c(1,2) n<-c(110000,138000) A.ref<-c(5.21,10.71) A.follow<-8.5 p.target<-20e-06 ci.mult.ref(k,n,A.ref,A.follow,p.target=p.target) k<-c(1,2,2) n<-c(110000,138000,170000) A.ref<-c(5.21,10.71,7.89) A.follow<-8.5 p.target<-20e-06 ci.mult.ref(k,n,A.ref,A.follow,p.target=p.target)
Function to compute upper Clopper-Pearson confidence limits of failure probabilities on the basis of differently sized reference products and failures tackled by countermeasures. Optionally, the required numbers of additional inspections for each reference product to reach a predefined target failure probability of the follower product are returned.
ci.mult.ref.cm(k, n, A.ref, A.follow, K, theta, alpha = 0.1, p.target = 1, prec = 2, tailcut = 1e-08, tol = 1e-12)ci.mult.ref.cm(k, n, A.ref, A.follow, K, theta, alpha = 0.1, p.target = 1, prec = 2, tailcut = 1e-08, tol = 1e-12)
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). |
A.follow |
size of follower product. |
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 |
theta |
vector of (different) effectivenesses of countermeasures. |
alpha |
alpha-level (1-alpha confidence level, default: 0.1). |
p.target |
target failure probability of follower product (optional). |
prec |
precision for greatest common divisor is 10^- |
tailcut |
probabilities for scaled failures smaller than |
tol |
tolerance of |
p.ref.cm |
vector of upper Clopper-Pearson confidence limits for each reference product with countermeasures (without the other reference products). |
p.mm.cm |
upper Clopper-Pearson confidence limit of the failure probability per mm^2 with countermeasures (on the basis of all reference products). |
p.follow.cm |
upper Clopper-Pearson confidence limit of the failure probability of the follower product with countermeasures (on the basis of all reference products). |
n.add.cm |
vector of required numbers of additional inspections for each reference product in order to reach p.target for the follower product with countermeasures. |
Daniel Kurz, Horst Lewitschnig
Maintainer: Horst Lewitschnig [email protected]
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.
phi.mult.ref
ci.mult.ref
phi.mult.ref.cm
#Reference product 1: 1 failure - failure tackled with 80% efficiency. #Reference product 2: 2 failures - 1 failure tackled with 80%, #1 failure with 60% efficiency. k<-c(1,2) K<-matrix(c(1,0,1,1),2,2,byrow=TRUE) n<-c(110000,138000) theta<-c(0.8,0.6) A.ref<-c(5.21,10.71) A.follow<-8.5 p.target<-20e-06 ci.mult.ref.cm(k,n,A.ref,A.follow,K,theta,p.target=p.target) #Reference product 1: 1 failure - failure tackled with 20% efficiency. #Reference product 2: 2 failures - 1 failure tackled with 20%, #1 failure with 40% efficiency. #Reference product 3: 2 failures - both tackled with 60% efficiency. k<-c(1,2,2) n<-c(110000,138000,170000) K<-matrix(c(1,0,0,1,1,0,0,0,2),3,3,byrow=TRUE) theta<-c(0.2,0.4,0.6) A.ref<-c(5.21,10.71,7.89) A.follow<-8.5 p.target<-20e-06 ci.mult.ref.cm(k,n,A.ref,A.follow,K,theta,p.target=p.target) #Reference product 1: 1 failure - failure tackled with 20% efficiency. #Reference product 2: 2 failures - 1 failure tackled with 40% efficiency, #1 failure without countermeasure. #Reference product 3: 3 failures - 1 failure tackled with 60% efficiency, #2 failures without countermeasures. k<-c(1,2,3) n<-c(110000,138000,170000) K<-matrix(c(1,0,0,0,1,0,0,0,1),3,3,byrow=TRUE) theta<-c(0.2,0.4,0.6) A.ref<-c(5.21,10.71,7.89) A.follow<-8.5 p.target<-20e-06 ci.mult.ref.cm(k,n,A.ref,A.follow,K,theta,p.target=p.target)#Reference product 1: 1 failure - failure tackled with 80% efficiency. #Reference product 2: 2 failures - 1 failure tackled with 80%, #1 failure with 60% efficiency. k<-c(1,2) K<-matrix(c(1,0,1,1),2,2,byrow=TRUE) n<-c(110000,138000) theta<-c(0.8,0.6) A.ref<-c(5.21,10.71) A.follow<-8.5 p.target<-20e-06 ci.mult.ref.cm(k,n,A.ref,A.follow,K,theta,p.target=p.target) #Reference product 1: 1 failure - failure tackled with 20% efficiency. #Reference product 2: 2 failures - 1 failure tackled with 20%, #1 failure with 40% efficiency. #Reference product 3: 2 failures - both tackled with 60% efficiency. k<-c(1,2,2) n<-c(110000,138000,170000) K<-matrix(c(1,0,0,1,1,0,0,0,2),3,3,byrow=TRUE) theta<-c(0.2,0.4,0.6) A.ref<-c(5.21,10.71,7.89) A.follow<-8.5 p.target<-20e-06 ci.mult.ref.cm(k,n,A.ref,A.follow,K,theta,p.target=p.target) #Reference product 1: 1 failure - failure tackled with 20% efficiency. #Reference product 2: 2 failures - 1 failure tackled with 40% efficiency, #1 failure without countermeasure. #Reference product 3: 3 failures - 1 failure tackled with 60% efficiency, #2 failures without countermeasures. k<-c(1,2,3) n<-c(110000,138000,170000) K<-matrix(c(1,0,0,0,1,0,0,0,1),3,3,byrow=TRUE) theta<-c(0.2,0.4,0.6) A.ref<-c(5.21,10.71,7.89) A.follow<-8.5 p.target<-20e-06 ci.mult.ref.cm(k,n,A.ref,A.follow,K,theta,p.target=p.target)
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.
ci.sas(k, n, A.ref, A.follow, alpha = 0.1, p.target = 1, atol = 1e-08)ci.sas(k, n, A.ref, A.follow, alpha = 0.1, p.target = 1, atol = 1e-08)
k |
vector of numbers of failures for each subset on reference product (total number of failures on reference product = sum of entries of |
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 |
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.
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 |
n.add.sas |
required number of additional inspections of the reference product in order to reach |
Daniel Kurz, Horst Lewitschnig
Maintainer: Horst Lewitschnig [email protected]
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.
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)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)
Function to compute upper Clopper-Pearson confidence limits of failure probabilities of follower products by means of separate area scaling (SAS) with failures tackled by countermeasures. Furthermore, the validity of the SAS in comparison to the classical area scaling (CAS) is evaluated taking into account the implemented countermeasures. 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 with countermeasures are returned.
ci.sas.cm(k, n, A.ref, A.follow, K, theta, alpha = 0.1, p.target = 1, atol = 1e-08)ci.sas.cm(k, n, A.ref, A.follow, K, theta, alpha = 0.1, p.target = 1, atol = 1e-08)
k |
vector of total numbers of failures for each subset on reference product (total number of failures on reference product = sum of entries of |
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). |
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 |
theta |
vector of (different) effectivenesses of countermeasures. |
alpha |
alpha-level (1-alpha confidence level, default: 0.1). |
p.target |
target failure probability of follower product (optional). |
atol |
tolerance of |
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.
p.cas.cm |
vector of upper Clopper-Pearson confidence limits of failure probabilities for each subset on reference product according to CAS with countermeasures. |
p.sas.cm |
vector of upper Clopper-Pearson confidence limits of failure probabilities for each subset on reference product according to SAS with countermeasures. |
p.follow.cas.cm |
upper Clopper-Pearson confidence limit of the failure probability of the follower product according to CAS with countermeasures. |
p.follow.sas.cm |
upper Clopper-Pearson confidence limit of the failure probability of the follower product according to SAS with countermeasures. |
delta.cm |
evidence factor against CAS with countermeasures. |
n.add.cas.cm |
required number of additional inspections of the reference product in order to reach |
n.add.sas.cm |
required number of additional inspections of the reference product in order to reach |
Daniel Kurz, Horst Lewitschnig
Maintainer: Horst Lewitschnig [email protected]
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.
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.
#Reference product: 1 failure. #Subset 1: 1 failure - failure tackled with 80% efficiency. #Subset 2: no failures. k<-c(1,0) K<-matrix(c(1,0),2,1) n<-100000 A.ref<-c(1,1) theta<-0.8 A.follow<-c(1,2) p.target<-20e-06 ci.sas.cm(k,n,A.ref,A.follow,K,theta,0.1,p.target) #Reference product: 3 failures. #Subset 1: 2 failures - 1 failure tackled with 80%, #1 failure with 70% efficiency. #Subset 2: 1 failure - failure tackled with 70% efficiency. #Subset 3: no failures. k<-c(2,1,0) K<-matrix(c(1,1,0,1,0,0),3,2,byrow=TRUE) n<-100000 A.ref<-c(2,3,4) theta<-c(0.8,0.7) A.follow<-c(1,2,3) p.target<-20e-06 ci.sas.cm(k,n,A.ref,A.follow,K,theta,0.1,p.target) #Reference product: 4 failures. #Subset 1: 2 failures - 1 failure tackled with 80% efficiency, #1 failure without countermeasure. #Subset 2: 1 failure - failure tackled with 70% efficiency. #Subset 3: 1 failure - failure without countermeasure. k<-c(2,1,1) K<-matrix(c(1,0,0,1,0,0),3,2,byrow=TRUE) n<-100000 A.ref<-c(2,3,4) theta<-c(0.8,0.7) A.follow<-c(1,2,3) p.target<-20e-06 ci.sas.cm(k,n,A.ref,A.follow,K,theta,0.1,p.target)#Reference product: 1 failure. #Subset 1: 1 failure - failure tackled with 80% efficiency. #Subset 2: no failures. k<-c(1,0) K<-matrix(c(1,0),2,1) n<-100000 A.ref<-c(1,1) theta<-0.8 A.follow<-c(1,2) p.target<-20e-06 ci.sas.cm(k,n,A.ref,A.follow,K,theta,0.1,p.target) #Reference product: 3 failures. #Subset 1: 2 failures - 1 failure tackled with 80%, #1 failure with 70% efficiency. #Subset 2: 1 failure - failure tackled with 70% efficiency. #Subset 3: no failures. k<-c(2,1,0) K<-matrix(c(1,1,0,1,0,0),3,2,byrow=TRUE) n<-100000 A.ref<-c(2,3,4) theta<-c(0.8,0.7) A.follow<-c(1,2,3) p.target<-20e-06 ci.sas.cm(k,n,A.ref,A.follow,K,theta,0.1,p.target) #Reference product: 4 failures. #Subset 1: 2 failures - 1 failure tackled with 80% efficiency, #1 failure without countermeasure. #Subset 2: 1 failure - failure tackled with 70% efficiency. #Subset 3: 1 failure - failure without countermeasure. k<-c(2,1,1) K<-matrix(c(1,0,0,1,0,0),3,2,byrow=TRUE) n<-100000 A.ref<-c(2,3,4) theta<-c(0.8,0.7) A.follow<-c(1,2,3) p.target<-20e-06 ci.sas.cm(k,n,A.ref,A.follow,K,theta,0.1,p.target)
Function to compute upper Clopper-Pearson confidence limits of failure probabilities on the basis of burn-in studies for each subset of a chip. Optionally, the required number of additional inspections for reaching a predefined target failure probability is returned.
ci.syn(k, n, alpha = 0.1, p.target = 1, tol = 1e-10)ci.syn(k, n, alpha = 0.1, p.target = 1, tol = 1e-10)
k |
vector of numbers of failures for each subset. |
n |
vector of numbers of inspections for each subset. |
alpha |
alpha-level (1-alpha confidence level, default: 0.1). |
p.target |
target failure probability (optional). |
tol |
tolerance of |
p.hat |
upper Clopper-Pearson confidence limit of the failure probability of the assembled devices. |
n.add |
required number of additional inspections of each subset for reaching |
Daniel Kurz, Horst Lewitschnig
Maintainer: Horst Lewitschnig [email protected]
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.
k<-c(0,1) n<-c(110000,330000) ci.syn(k,n,0.1,20e-06) k<-c(1,0,1,5) n<-c(330000,240000,240000,400000) ci.syn(k,n,0.1,20e-06)k<-c(0,1) n<-c(110000,330000) ci.syn(k,n,0.1,20e-06) k<-c(1,0,1,5) n<-c(330000,240000,240000,400000) ci.syn(k,n,0.1,20e-06)
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.
ci.syn.cm(k, n, K, theta, alpha = 0.1, p.target = 1, tol = 1e-10)ci.syn.cm(k, n, K, theta, alpha = 0.1, p.target = 1, tol = 1e-10)
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 |
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 |
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 |
Daniel Kurz, Horst Lewitschnig
Maintainer: Horst Lewitschnig [email protected]
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.
#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)#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)
Function to compute the greatest common divisor of the chip sizes of the reference products at a fixed precision.
gcd.mult.ref(A, prec = 2)gcd.mult.ref(A, prec = 2)
A |
vector of chip sizes for each reference product (in mm^2). |
prec |
precision for greatest common divisor is 10^- |
A.gcd |
greatest common divisor of the sizes in mm^2 (at specified precision). |
Daniel Kurz, Horst Lewitschnig
Maintainer: Horst Lewitschnig [email protected]
A<-c(48, 30, 42) gcd.mult.ref(A) A<-c(2.2, 3.01, 5) gcd.mult.ref(A, prec = 2) gcd.mult.ref(A, prec = 1) gcd.mult.ref(A, prec = 0)A<-c(48, 30, 42) gcd.mult.ref(A) A<-c(2.2, 3.01, 5) gcd.mult.ref(A, prec = 2) gcd.mult.ref(A, prec = 1) gcd.mult.ref(A, prec = 0)
Function to scale the numbers of failures 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.
phi.mult.ref(k, n, A.ref, prec = 2, tailcut = 1e-08)phi.mult.ref(k, n, A.ref, prec = 2, tailcut = 1e-08)
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). |
prec |
precision for greatest common divisor is 10^- |
tailcut |
probabilities for scaled failures smaller than |
phi |
data frame with possible numbers of failures |
A.gcd |
greatest common divisor of the sizes of the reference products. |
Daniel Kurz, Horst Lewitschnig
Maintainer: Horst Lewitschnig [email protected]
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.
ci.mult.ref
phi.mult.ref.cm
ci.mult.ref.cm
k<-c(1,2) n<-c(10,15) A.ref<-c(2,3) phi.mult.ref(k,n,A.ref) k<-c(1,1) n<-c(110000,220000) A.ref<-c(5.21,10.71) phi.mult.ref(k,n,A.ref) k<-c(1,2,3,4) n<-c(10,15,20,30) A.ref<-c(1,2,3,4) phi.mult.ref(k,n,A.ref)k<-c(1,2) n<-c(10,15) A.ref<-c(2,3) phi.mult.ref(k,n,A.ref) k<-c(1,1) n<-c(110000,220000) A.ref<-c(5.21,10.71) phi.mult.ref(k,n,A.ref) k<-c(1,2,3,4) n<-c(10,15,20,30) A.ref<-c(1,2,3,4) phi.mult.ref(k,n,A.ref)
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.
phi.mult.ref.cm(k, n, A.ref, K, theta, prec = 2, tailcut = 1e-08)phi.mult.ref.cm(k, n, A.ref, K, theta, prec = 2, tailcut = 1e-08)
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 |
theta |
vector of (different) effectivenesses of countermeasures. |
prec |
precision for greatest common divisor is 10^- |
tailcut |
probabilities for scaled failures smaller than |
phi.cm |
data frame with possible number of failures |
A.gcd |
greatest common divisor of the sizes of the reference products. |
Daniel Kurz, Horst Lewitschnig
Maintainer: Horst Lewitschnig [email protected]
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.
phi.mult.ref
ci.mult.ref
ci.mult.ref.cm
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)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)
Function to compute probability of having a certain number of failures out of min(n) devices, which are randomly assembled out of a certain number of chip subsets.
phi.syn(k, n)phi.syn(k, n)
k |
vector of numbers of failures for each subset. |
n |
vector of numbers of inspections for each subset. |
phi |
data frame with possible numbers of failures (out of |
Daniel Kurz, Horst Lewitschnig
Maintainer: Horst Lewitschnig [email protected]
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.
k<-c(1,2) n<-c(10,15) phi.syn(k,n) k<-c(0,1,1,1) n<-c(110000,220000,150000,330000) phi.syn(k,n)k<-c(1,2) n<-c(10,15) phi.syn(k,n) k<-c(0,1,1,1) n<-c(110000,220000,150000,330000) phi.syn(k,n)
Function to compute the probability of having a certain number of failures out of min(n) randomly assembled devices with countermeasures.
phi.syn.cm(k, n, K, theta)phi.syn.cm(k, n, K, theta)
k |
vector of total 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 of 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 |
theta |
vector of (different) effectivenesses of countermeasures. |
phi.cm |
data frame with possible numbers of failures (out of |
Daniel Kurz, Horst Lewitschnig
Maintainer: Horst Lewitschnig [email protected]
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.
k<-c(0,1) K<-matrix(c(0,1),2,1,byrow=TRUE) theta<-0.8 n<-c(110000,330000) phi.syn.cm(k,n,K,theta) k<-c(1,1,2) K<-matrix(c(0,0,0,1,1,1),3,2,byrow=TRUE) theta<-c(0.7,0.5) n<-c(10,15,20) phi.syn.cm(k,n,K,theta)k<-c(0,1) K<-matrix(c(0,1),2,1,byrow=TRUE) theta<-0.8 n<-c(110000,330000) phi.syn.cm(k,n,K,theta) k<-c(1,1,2) K<-matrix(c(0,0,0,1,1,1),3,2,byrow=TRUE) theta<-c(0.7,0.5) n<-c(10,15,20) phi.syn.cm(k,n,K,theta)