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Book Part Shocks, Scans, and Reliability Systems(Springer New York, 2024) Eryilmaz,S.This chapter summarizes the close connection between one of the widely studied shock models known as δ-shock model and runs/scans. Under discrete time setting, i.e., when the shocks occur according to a binomial process, the linkage between the lifetime of the system under the shock model and the waiting time for the first scan is presented. Such a useful connection may create a new perspective to study the reliability properties of the system under the δ-shock model. © Springer Science+Business Media, LLC, part of Springer Nature 2024.Book Part Discrete Scan Statistics Generated by Dependent Trials and Their Applications in Reliability(Springer New York, 2024) Eryilmaz,S.; Yalcin,F.The chapter is concerned with discrete scan statistic based on a sequence of dependent binary trials. In particular, the existing results are reviewed for the distribution of the discrete scan statistic based on a sequence of exchangeable binary trials. The results are discussed in the context of the reliability of the linear consecutive-k-within-m-out-of-n:F system, and a new exact formula for the reliability of the linear consecutive-2-within-m-out-of-n:F system that consists of arbitrarily dependent components is presented. © Springer Science+Business Media, LLC, part of Springer Nature 2024.
