Statistical Evaluation of Learning Factor in Reliability Studies
A mathematical formulation is developed which allows the statistical evaluation of certain features of the probability distribution of the ratio between two random variables as in the determination of learning factors. This evaluation is of the mode, an s-confidence band for the ratio, and the effect of sample size.
Confidence Intervals for the Ratio of Two Poisson Means and Poisson Predictor Intervals
Easy-to-use charts are presented for confidence intervals for the ratio of two Poisson mean occurrence rates and for predictor intervals for the future value of a Poisson random variable, given a previously observed value. The use of the charts is illustrated and their theoretical basis is given.
CONFIDENCE INTERVALS FOR A PROPORTION
Tables of confidence intervals for a proportion based on the sample proportion are presented, calculated by a slight modification of the method proposed by Sterne (1954), for fixed sample sizes up to 30 and confidence coefficients of 0 90, 0 95 and 0 99. This system is compared, especially in shortness, with Sterne's system, Clopper & Pearson's (1934), and another, intermediate system. It is assumed that a random sample of fixed size n is drawn from an infinite population containing a proportion oT of individuals with a given characteristic, that r individuals are observed to have the characteristic, and that it is desired to estimate 7 by means of a two-sided confidence interval. While relatively tedious to calculate, Sterne's system and its modification have in common the advantage that no system is possible which has shorter total length of the n + 1 confidence intervals for r = 0, 1, .. ., n. However, they are at a disadvantage if one