# Upper Clopper-Pearson confidence limits under chip synergies and countermeasures 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. ```r 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). ## Returns - **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. ## Author(s) Daniel Kurz, Horst Lewitschnig Maintainer: Horst Lewitschnig horst.lewitschnig@infineon.com ## See Also `phi.syn` `ci.syn` `phi.syn.cm` ## Examples ```r #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) ```

ci.syn.cm function