## Runs and scans with applicationsExpert practical and theoretical coverage of runs and scans This volume presents both theoretical and applied aspects of runs and scans, and illustrates their important role in reliability analysis through various applications from science and engineering. Runs and Scans with Applications presents new and exciting content in a systematic and cohesive way in a single comprehensive volume, complete with relevant approximations and explanations of some limit theorems. The authors provide detailed discussions of both classical and current problems, such as: * Sooner and later waiting time * Consecutive systems * Start-up demonstration testing in life-testing experiments * Learning and memory models * "Match" in genetic codes Runs and Scans with Applications offers broad coverage of the subject in the context of reliability and life-testing settings and serves as an authoritative reference for students and professionals alike. |

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### Contents

Waiting for the First Run Occurrence | 9 |

Vlll | 52 |

Applications | 71 |

Copyright | |

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### Common terms and phrases

Analysis Antzoulakos Applications asymptotic Bernoulli trials binary sequence binary trials compound Poisson conditional distribution confidence interval cumulative distribution function denote derived distribution function distribution of order double generating function enumeration scheme estimate evaluation example expression F system failure run Fibonacci numbers Fibonacci Quarterly formula geometric distribution Glaz Godbole Hirano initial conditions Institute of Statistical integers Kotz Koutras and Alexandrou Later geometric distribution length k2 Markov chain matrix method Mn,k negative binomial distribution Nn,k non-overlapping number of successes number of trials observed obtain oooo oooo oooo order fci order k/m outcomes overlapping P(Yt Papastavridis Philippou Poisson approximation probability generating function probability mass function random variables recurrence relations recursive scheme reliability run of length sample Section start-up demonstration testing Statistical Mathematics success run transition probability trinomial Type I binomial Type I negative vectors Viveros and Balakrishnan waiting time problems