Binomial Distribution: Hypothesis Testing, Confidence Intervals (CI), and Reliability with Implementation in S-PLUS

Report No. ARL-TR-5214
Authors: Joseph C. Collins
Date/Pages: June 2010; 43 pages
Abstract: System requirements can be expressed in terms of an upper (lower) limit on the probability of failure (success). Statistical analysis of such binary (0/1, success/failure, go/no-go) data typically requires point and interval estimation and inference or hypothesis tests on the associated event probability. For identical independent trials, the proportion observed serves as an estimate of the event rate. Based on the method of Clopper-Pearson (CP) and the likelihood ratio (LR) technique properties of the binomial distribution are used to derive interval estimates, which are in turn used in inference. An application is the determination of sample size and maximum permissible number of failures (nf) required to establish a specific reliability (probability of success) with given probability (confidence).
Distribution: Approved for public release
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Last Update / Reviewed: June 1, 2010