The Open Mathematics, Statistics and Probability Journal

2017, 8 : 1-6
Published online 2017 February 28. DOI: 10.2174/1876527001708010001
Publisher ID: TOSPJ-8-1

RESEARCH ARTICLE
 On Limited Length Binary Strings with an Application in Statistical Control

F.S. Makri1, * and Z.M. Psillakis2

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

ABSTRACT

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.