CHANCE OF ALL SUCCESS FOR INDEPENDENT BINOMIAL EVENTS WITH LARGE SUCCESS PROBABILITIES.
SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS
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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 n1 - 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 n1 - p or .25 and the relative error is less than one percent when n1 - 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
- Statistics and Probability
- Manufacturing and Industrial Engineering and Control of Production Systems