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• W2949116816 abstract "Many systems experience gradual degradation while simultaneously being exposed to a stream of random shocks of varying magnitudes that eventually cause failure when a shock exceeds the residual strength of the system. In this paper, we present a family of stochastic processes, called shock-degradation processes, that describe this failure mechanism. In our failure model, system strength follows a geometric degradation process. The degradation process itself is any Levy process, that is, any stochastic process with stationary independent increments. The shock stream is a Frechet stochastic process, a process derived from the Frechet extreme-value distribution. Finally, the shock-degradation process is a convolution of the Frechet shock process and any one of the candidate degradation processes. The system fails at the first occasion when a shock takes system strength across a threshold at zero. The paper presents results for Wiener diffusion processes and gamma processes as examples of Levy degradation processes. The paper develops key statistical properties of the process model and its survival distribution, including several that are important for its practical application. As the failure mechanism is a first hitting time event, applications that require regression structures fall within the domain of threshold regression methodology." @default.
• W2949116816 created "2019-06-27" @default.
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• W2949116816 date "2019-06-11" @default.
• W2949116816 modified "2023-09-24" @default.
• W2949116816 title "A new class of survival distribution for degradation processes subject to shocks" @default.
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• W2949116816 doi "https://doi.org/10.1186/s40488-019-0095-1" @default.
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