On Success Runs of Length Exceeded a Threshold

Frosso S. Makri () and Zaharias M. Psillakis ()
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Frosso S. Makri: University of Patras
Zaharias M. Psillakis: University of Patras

Methodology and Computing in Applied Probability, 2011, vol. 13, issue 2, 269-305

Abstract: Abstract Consider a sequence of n two state (success-failure) trials with outcomes arranged on a line or on a circle. The elements of the sequence are independent (identical or non identical distributed), exchangeable or first-order Markov dependent (homogeneous or non homogeneous) random variables. The statistic denoting the number of success runs of length at least equal to a specific length (a threshold) is considered. Exact formulae, lower/upper bounds and approximations are obtained for its probability distribution. The mean value and the variance of it are derived in an exact form. The distributions and the means of an associated waiting time and the length of the longest success run are provided. The reliability function of certain general consecutive systems is deduced using specific probabilities of the studied statistic. Detailed application case studies, covering a wide variety of fields, are combined with extensive numerical experimentation to illustrate further the theoretical results.

Keywords: Success runs; Longest run length; Waiting time; Linear and circular binary sequences; Bernoulli trials; Poisson trials; Exchangeable trials; Markov chain; Reliability of consecutive systems; Exceedances; Polya-Eggenberger sampling scheme; Primary 60E05, 62E15; Secondary 60C05, 60G09, 60J10 (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s11009-009-9147-1

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