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BOUNDARY CROSSING PROBABILITIES FOR THE CUMULATIVE SAMPLE MEAN

Published online by Cambridge University Press:  08 March 2017

Dashi I. Singham Open the ORCID record for Dashi I. Singham [Opens in a new window]  and
Michael P. Atkinson
Dashi I. Singham
Affiliation:
Operations Research Department, Naval Postgraduate School, Monterey, CA 93943, USA E-mail: [email protected]
Michael P. Atkinson
Affiliation:
Operations Research Department, Naval Postgraduate School, Monterey, CA 93943, USA E-mail: [email protected]
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Abstract

We develop a new measure of reliability for the mean behavior of a process by calculating the probability the cumulative sample mean will stay within a given distance from the true mean over a period of time. This probability is derived using boundary-crossing properties of Brownian bridges. We derive finite sample results for independent and identically distributed normal data, limiting results for data meeting a functional central limit theorem, and draw parallels to standard normal confidence intervals. We deliver numerical results for i.i.d., dependent, and queueing processes.

Keywords

applied probabilityreliability theorysimulationBrownian bridge
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 32 , Issue 2 , April 2018 , pp. 275 - 295
Copyright
Copyright © Cambridge University Press 2017 

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