Downloaded from https://www.everyspec.com ADS-79D-HDBK deviation is temporarily ignored because that is not the point that the author or instructor is then explaining, and (3) those that a great understanding or prior knowledge exist about the variance of the anticipated population. Given known standard deviation and significance level, the sample size can be easily determined using the aforementioned equation. If the error tolerance is reasonable, the required sample size can be optimized. I.3.5 Test on Population Proportion . It is often necessary to construct confidence intervals on a population proportion.
For example, suppose that a random sample of size n has been taken from a large population and that (X ≤ n ) observations in this sample belong to a class of interest. Then = X/ n is a point estimator of the proportion of the population p that belongs to this class. Binomial or Bernoulli trials are often used in Population Proportion test. In Bernoulli trials, it assumes that (1) each trial results in either a success or a failure, (2) the probability of success does not change from trial to trial, and (3) the outcome of one trial does not affect the outcome of any other trial.
If the aforementioned conditions hold, the probability of exactly s successes out of n Bernoulli trials can be calculated via Binomial distribution, where, n is the total number of Bernoulli trials, s is the number of successes trials, R is the probability of success in each trial for the CI/HI to correctly categorize a faulted/unfaulted component, and Q is the probability of failure for the CI/HI to correctly categorize a faulted/un-faulted component in each trial. Accordingly, the cumulative Binomial distribution function is: which gives the probability of up to and including S 1 successes in n trials, when each trial has a probability of succeeding of R .
Given the number of failures, r , or the number of successes, s , in n Bernoulli trials, the average value of reliability can be estimated, from: The confidence limits on R can also be determined, upon a given significance level. The lower one-sided confidence limit on the reliability, R L1 may be obtained from: Similarly, the upper one-sided confidence limit on the reliability, R U1 may be obtained from: I.3.6 Reliability Demonstration Test . Reliability demonstration test is often employed to illustrate that a component or system meets the design requirement and possesses a desirable level of 151