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New shock models based on the generalized Polya process

Title
New shock models based on the generalized Polya process
Authors
Cha, Ji HwanFinkelstein, Maxim
Ewha Authors
차지환
SCOPUS Author ID
차지환scopus
Issue Date
2016
Journal Title
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
ISSN
0377-2217JCR Link1872-6860JCR Link
Citation
vol. 251, no. 1, pp. 135 - 141
Keywords
Generalized Polya processExtreme shock modelCumulative shock modelCombined shock modelTime-dependent wear
Publisher
ELSEVIER SCIENCE BV
Indexed
SCIE; SCOPUS WOS scopus
Abstract
Various shock models have been extensively studied in the literature, mostly under the assumption of the Poisson process of shocks. In the current paper, we study shock models under the generalized Polya process (GPP) of shocks, which has been recently introduced and characterized in the literature (see Konno (2010) and Cha, 2014). Distinct from the widely used nonhomogeneous Poisson process, the important feature of this process is the dependence of its stochastic intensity on the number of previous shocks. We consider the extreme shock model, where each shock is catastrophic for a system with probability p(t) and is harmless with the complementary probability q(t) = 1 - p(t). The corresponding survival and the failure rate functions are derived and analyzed. These results can be used in various applications including engineering, survival analysis, finance, biology and so forth. The cumulative shock model, where each shock results in the increment of wear and a system's failure occurs when the accumulated wear reaches some boundary is also considered. A new general concept describing the dependent increments property of a stochastic process is suggested and discussed with respect to the GPP. (C) 2015 Elsevier B.V. All rights reserved.
DOI
10.1016/j.ejor.2015.11.032
Appears in Collections:
자연과학대학 > 통계학전공 > Journal papers
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