On Limited Length Binary Strings with an Application in Statistical Control

F.S. Makri1, *, Z.M. Psillakis2
1 Department of Mathematics, University of Patras, 26500 Patras, Greece
2 Department of Physics, University of Patras, 26500 Patras, Greece

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© 2017 Makri and Psillakis

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Mathematics, University of Patras, 26500 Patras, Greece; Tel: 0030-2610-996738; E-mail:


In a 0 - 1 sequence of Markov dependent trials we consider a statistic which counts strings of a limited length run of 0s between subsequent 1s. Its probability mass function is used to determine the chance that a stochastic process remains or not in statistical control. Illustrative numerics are presented.

Keywords: Binary strings, runs, overlapping counting, Markov chain, Statistical control.