Failure distributions of shock models

Gottlieb, Gary

doi:10.1017/s0021900200033854

Cited by 7 publications

(2 citation statements)

References 4 publications

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“…Remark 1: It is easily derived that is iff is non-increasing in for all (see Gottlieb [14]). Furthermore, using Lemma 3.7 of Barlow and Proschan [3], we can show that is non-increasing in for all .…”

Section: Optimizationmentioning

confidence: 99%

Extended Optimal Replacement Policy for a Two-Unit System With Shock Damage Interaction

et al. 2015

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In this paper, we consider a system consisting of two major units, A and B, each subject to two types of shocks that occur according to a non-homogeneous Poisson process. A type II shock causes a complete system failure which is corrected by a replacement; and a type I shock causes a unit A minor failure, which is rectified by a minimal repair. The shock type probability is age-dependent. Each unit A minor failure results in a random amount of damage to unit B. Such a damage to unit B can be accumulated to a specified level of the complete system failure. Moreover, unit B with a cumulative damage of level may become minor failed with probability at each unit A minor failure, and fixed by a minimal repair. We consider a more general replacement policy where the system is replaced at age , or the th type I shock, or first type II shock, or when the total damage to unit B exceeds a specified level, whichever occurs first. We determine the optimal policy of and to minimize the s-expected cost per unit time. We present some numerical examples, and show that our model is the generalization of many previous maintenance models in the literature.Index Terms-Cumulative damage model, optimization, replacement policy., shock model.

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Section: Optimizationmentioning

confidence: 99%

Extended Optimal Replacement Policy for a Two-Unit System With Shock Damage Interaction

et al. 2015

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“…For systems subject only to sporadic jump damages, a compound Poisson process, a stochastic process with independent and identically distributed (i.i.d) jumps that occur according to a Poisson process, is one of the appropriate candidates to model the cumulative damages. Abdel‐Hameed and Gottlieb introduced the life distribution and its properties for systems subject to pure jump damage processes.…”

Section: Introductionmentioning

confidence: 99%

Life distribution analysis based on Lévy subordinators for degradation with random jumps

Yin

Feng

Coit

2015

Naval Research Logistics

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Abstract:For a component or a system subject to stochastic degradation with sporadic jumps that occur at random times and have random sizes, we propose to model the cumulative degradation with random jumps using a single stochastic process based on the characteristics of Lévy subordinators, the class of nondecreasing Lévy processes. Based on the inverse Fourier transform, we derive a new closed-form reliability function and probability density function for lifetime, represented by Lévy measures. The reliability function derived using the traditional convolution approach for common stochastic models such as gamma degradation process with random jumps, is revealed to be a special case of our general model. Numerical experiments are used to demonstrate that our model performs well for different applications, when compared with the traditional convolution method. More importantly, it is a general and useful tool for life distribution analysis of stochastic degradation with random jumps in multidimensional cases.

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Instandhaltungsmodelle — Eine Übersicht

Bosch

Jensen

1983

OR Spektrum

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Failure distributions of shock models

Cited by 7 publications

References 4 publications

Extended Optimal Replacement Policy for a Two-Unit System With Shock Damage Interaction

Extended Optimal Replacement Policy for a Two-Unit System With Shock Damage Interaction

Life distribution analysis based on Lévy subordinators for degradation with random jumps

Instandhaltungsmodelle — Eine Übersicht

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