SAMPLING FOR RELIABILITY DETERMINATION, AN IMPROVED SCHEME.
Abstract
A unique solution is presented for the ancient sampling problem posed as follows: One is to test a finite random sample from a large population for some property that an unknown fraction of the population possesses. Required: To deduce the most accurate possible probabilistic statements in the following sense. For a specified probability that the unknown fraction be larger than some lower limit, calculate from the test result the largest possible lower limit that will have at least this probability and the smallest possible upper limit that will have at most this probability. Similarly, specify narrowest possible ranges for upper limits. These formulas can then be applied to determine for specified lower and upper limits two probabilities for their enclosure of the unknown fraction, the larger of which is the lowest possible upper limit and the smaller of which is the largest possible lower limit. It must be understood that these probabilistic statements refer to the conceptual or actual results of continued sampling for which the enclosure probabilities are held constant and the differing test results give a distribution of lower and upper limits. A 'best' formula is also given which lies between the others and has a zero value of a reasonably defined average error. Use of the proposed scheme will reduce needed sample sizes as compared to usual statistical procedure in which only 'pessimistic' relations are used. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1964
- Accession Number
- AD0607909
Entities
People
- W. C. Beckham
Organizations
- Air Force Research Laboratory