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Citation - WoS: 27
Citation - Scopus: 31
Generalized Extreme Shock Models and Their Applications
(Taylor & Francis inc, 2020) Bozbulut, Ali Riza; Eryilmaz, Serkan
In the classical extreme shock model, the system fails due to a single catastrophic shock. In this paper, by assuming different arrival patterns of the shocks, two new types of extreme shock models are introduced. In these models, m possible sources may exert shocks on the system. Both models reduce to the classical extreme shock model when m = 1. Assuming phase-type distribution for times between successive shocks, we obtain survival functions and mean time to failure values of the system under new models. Two different optimization problems are also considered to determine the optimal number of sources.
Citation - WoS: 4
Citation - Scopus: 6
Statistical Inference for a Class of Startup Demonstration Tests
(Taylor & Francis inc, 2019) Eryilmaz, Serkan
In this article, we develop a general statistical inference procedure for the probability of successful startup p in the case of startup demonstration tests when only the number of trials until termination of the experiment are observed. In particular, we define a class of startup demonstration tests and present expectation-maximization (EM) algorithm to get the maximum likelihood estimate of p for this class. Most of well-known startup testing procedures are involved in this class. Extension of the results to Markovian startups is also presented.