# Upper Clopper-Pearson confidence limits for area scaling with differently sized reference products 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. ```r ci.mult.ref(k, n, A.ref, A.follow, alpha = 0.1, p.target = 1, prec = 2, tailcut = 1e-08, tol = 1e-12) ``` ## 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). - `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^-`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. - `tol`: tolerance of `uniroot`-function used for computing failure probability per greatest common chip size (default: 1e-12). ## Returns - **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. ## 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. ## Author(s) Daniel Kurz, Horst Lewitschnig Maintainer: Horst Lewitschnig horst.lewitschnig@infineon.com ## See Also `phi.mult.ref` `ci.mult.ref.cm` `phi.mult.ref.cm` ## Examples ```r 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) ```

ci.mult.ref function