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Mean recurrence times for k successes within m trials

Published online by Cambridge University Press:  14 July 2016

Raymond J. Huntington
Raymond J. Huntington*
Affiliation:
A.T. & T., Long Lines Business Research
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Abstract

Given an unlimited sequence of Bernoulli trials, let E be the recurrent event that k or more successes occur within m consecutive trials in the sequence. Let μk, m denote the mean recurrence time for E. Previous work finds expressions for μk, m for limited values of k and m. The present paper derives a closed expression for μk, m for all k, m. Tables for μk, m are also presented.

Keywords

WAITING TIMERECURRENCE TIMESBERNOULLI TRIALSSMALLEST NUMBER OF TRIALSCLUSTER
Type
Short Communications
Information
Journal of Applied Probability , Volume 13 , Issue 3 , September 1976 , pp. 604 - 607
Copyright
Copyright © Applied Probability Trust 1976 

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References

Feller, W. (1968) An Introduction to Probability Theory and its Applications, Vol. I, 3rd edn. Wiley, New York.Google Scholar
Greenberg, I. (1970) The first occurrence of n successes in N trials. Technometrics 12, 627–634.Google Scholar
Roberts, S. W. (1958) Properties of control chart zone tests. Bell System Tech. J. 37, 83.Google Scholar
Saperstein, B. (1973) On the occurrence of n successes within N Bernoulli trials. Technometrics 15, 809–818.Google Scholar
Troxell, J. R. (1972) An Investigation of Suspension Systems for Small Scale Inspections. Ph.D. Dissertation, Rutgers University.Google Scholar