Fluctuation Analysis of a Soft-Extreme Shock Reliability Model

Jewgeni H. Dshalalow () and Ryan T. White
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Jewgeni H. Dshalalow: Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA
Ryan T. White: Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA

Mathematics, 2022, vol. 10, issue 18, 1-33

Abstract: In this paper, we deal with a mixed reliability system decaying from natural wear, occasional soft and hard shocks that eventually lead the system to failure. The aging process alone is linear and it is escalated through soft shocks such that they lead to the system’s soft failure when the combined damage exceeds a threshold M . The other threat is that posed by occasional hard shocks. When the total number of them identified as critical (each critical shock exceeds a fixed threshold H ) reaches N , the system becomes disabled. With N = 1 , a critical shock is extreme . The arrival stream of shocks is a renewal process marked by soft and hard shocks. We establish a formula for a closed form functional containing system’s time-to-failure , the state of the system upon its failure, and other useful statistical characteristics of the system using and embellishing fluctuation analysis and operational calculus. Special cases provide tame expressions that are computed and validated by simulation.

Keywords: reliability system with degradation; soft shocks; critical shocks; extreme shocks; fatal shocks; random walk analysis; fluctuation theory; marked renewal process; position-dependent marking; marked Poisson process; time-to-failure; lifetime of the system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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