On the Time-Dependent Delta-Shock Model Governed by the Generalized PóLya Process

Goyal, Dheeraj; Hazra, Nil Kamal; Finkelstein, Maxim

doi:10.1007/s11009-021-09880-8

Cited by 26 publications

(15 citation statements)

References 33 publications

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“…iii) The GPP with parameters {𝛼, 𝛽, 𝜆(𝑡)} for 𝛼 = 1 and 𝜆(𝑡) = 1∕(𝑏 + 𝑡), 𝑏 > 0 is the Polya process (see 15 ). On the basis of the lemma in ref., 15 the following properties of GPP with the set of parameters {𝛼, 𝛽, 𝜆(𝑡)}, 𝛼 > 0, 𝛽 > 0 can be obtained: i) The distribution of 𝑁(𝑡) is:…”

Section: System Description and Preliminariesmentioning

confidence: 99%

“…These products will take more time to recover from the damage caused by shocks, whereas the assumption of a fixed δ threshold is no longer qualified for such cases. As a result, Goyal et al 15 derived a new δ-shock model by assuming the recovery time as an increasing function of time. The greater part of the literature on shock models employs the Poisson process to model the arrival of random shocks.…”

Section: Introductionmentioning

confidence: 99%

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Reliability modeling of dependent competing failure processes based on time‐dependent threshold level δ and degradation rate changes

Lyu

et al. 2023

Quality & Reliability Eng

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A new reliability model for dependent competing failure processes is proposed. The reliability model uses the generalized Polya process (GPP) to model the arrival of shocks and considers the degradation rate change. Most systems fail due to performance degradation and external environment shocks. On the one hand, soft failure occurs when the total amount of degradation, including continuous degradation and sudden degenerate increment, exceeds the soft failure threshold level. On the other hand, hard failure occurs when the time interval between two successive shocks is less than the recovery time. As time progresses and natural degradation, the time for a system to recover from damage due to shocks tends to increase gradually. However, conventional models usually regard recovery time as a constant, unrealistic in many practical situations. For this purpose, an increment‐dependent shock process is considered. A hard failure reliability model with recovery time is calculated using the GPP to describe the shock arrival process. On this basis, combined with the deduced soft failure function, the analytical solution of the reliability model is obtained. Finally, a numerical example based on the micro‐electro mechanical systems is conducted to illustrate the effectiveness of the proposed model.

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Section: System Description and Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reliability modeling of dependent competing failure processes based on time‐dependent threshold level δ and degradation rate changes

Lyu

et al. 2023

Quality & Reliability Eng

View full text Add to dashboard Cite

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“…Eryilmaz and Kan 12 assessed reliability for the case when times between successive shocks and the magnitudes of shocks have discrete phase-type distributions. Goyal et al 13 considered a time-dependent δ -shock model. They assumed that shocks occur according to the generalized Polya process that contains the homogeneous Poisson process ( HPP ), the non-homogeneous Poisson process ( NHPP ) and the Polya process as particular cases.…”

Section: Introductionmentioning

confidence: 99%

Reliability analysis and optimal replacement for a k-out-of-n system under a δ-shock model

Lorvand

Kelkinnama

2022

Proceedings of the Institution of Mechanical Engineers, Part O:

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Consider a k-out-of- n system which is subject to shocks that arrive at random times. This study develops [Formula: see text]-shock model, among the variants of well-known shock models, for such system which consists of independent components. In a [Formula: see text]-shock model, the system fails when the inter-arrival between two consecutive shocks is less than a critical threshold value of [Formula: see text]. Depending on the number of components that fail due to the occurrence of the shocks, we introduce two [Formula: see text]-shock models. The reliability function and mean time to failure of the system are discussed when the time between shocks has an arbitrary distribution. Furthermore, the problem of finding the optimal preventive time concerned with minimizing a mean cost per unit time is investigated. Numerical examples based on a simulation study are also provided to illustrate theoretical achievement.

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“…Moreover, if the magnitude of an earthquake exceeds a fixed threshold level, then the bridge entirely collapses. In our recent paper (Goyal et al [18]), the first step in considering a more general model of the current paper was made when δ was assumed to depend only on the arrival time of a shock.…”

Section: Introductionmentioning

confidence: 99%

On the general $$\delta $$-shock model

Goyal

Hazra

Finkelstein

2022

TEST

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The δ-shock model is one of the basic shock models which has a wide range of applications in reliability, finance and related fields. In existing literature, it is assumed that the recovery time of a system from the damage induced by a shock is constant as well as the shocks magnitude. However, as technical systems gradually deteriorate with time, it takes more time to recover from this damage, whereas the larger magnitude of a shock also results in the same effect. Therefore, in this paper, we introduce a general δ-shock model when the recovery time depends on both the arrival times and the magnitudes of shocks. Moreover, we also consider a more general and flexible shock process, namely, the Poisson generalized gamma process. It includes the homogeneous Poisson process, the nonhomogeneous Poisson process, the Pólya process and the generalized Pólya process as the particular cases. For the defined survival model, we derive the relationships for the survival function and the mean lifetime and study some relevant stochastic properties. As an application, an example of the corresponding optimal replacement policy is discussed.

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On the Time-Dependent Delta-Shock Model Governed by the Generalized PóLya Process

Cited by 26 publications

References 33 publications

Reliability modeling of dependent competing failure processes based on time‐dependent threshold level δ and degradation rate changes

Reliability modeling of dependent competing failure processes based on time‐dependent threshold level δ and degradation rate changes

Reliability analysis and optimal replacement for a k-out-of-n system under a δ-shock model

On the general $$\delta $$-shock model

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