
Accession Number : AD0679681
Title : CHANCE OF ALL SUCCESS FOR INDEPENDENT BINOMIAL EVENTS WITH LARGE SUCCESS PROBABILITIES.
Descriptive Note : Technical rept.,
Corporate Author : SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS
Personal Author(s) : Walsh,John E.
Report Date : 16 SEP 1968
Pagination or Media Count : 8
Abstract : Consider reliability situations where all of n independent steps or operations must be satisfactory (successes) if the overall operation is to be satisfactory. The interest is in reliability levels that are at least moderately high. That is, the probability of obtaining successes for all steps and operations is at least moderately near unity. An approximate expression, also sharp upper and lower bounds, are developed for the probability of all successes. These results are applicable when n(1  p) < 1, where p is the arithmetic average of the n probabilities of success for the steps and operations. The approximate expression is near the bounds when n(1  p) = or < .25 and the relative error is less than one percent when n(1  p) = or < .17; then, the true probability is at least .75 and at least .83, respectively. These results depend only on n and p. They are applicable for all n = or > 1 and any set of success probabilities. (Author)
Descriptors : (*RELIABILITY, *PROBABILITY), APPROXIMATION(MATHEMATICS), STATISTICAL ANALYSIS
Subject Categories : Statistics and Probability
Mfg & Industrial Eng & Control of Product Sys
Distribution Statement : APPROVED FOR PUBLIC RELEASE