Minimal repair under a step-stress test

Kamps, Udo; Kateri, Maria

doi:10.1016/j.spl.2009.03.020

Cited by 18 publications

(9 citation statements)

References 30 publications

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“…Related recent results in settings of generalized order statistics can be found in Xie and Hu (2008), Balakrishnan et al (2009), Burkschat andLenz (2009), andHashemi et al (2010). This follows from the distribution theoretical relation (X * i+1:n , .…”

Section: Mixture Representations Using Additional Information About Amentioning

confidence: 72%

Dynamic Signatures of Coherent Systems Based on Sequential Order Statistics

Burkschat¹,

Navarro²

2013

J. Appl. Probab.

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Sequential order statistics can be used to describe the ordered lifetimes of components in a system, where the failure of a component may affect the performance of remaining components. In this paper mixture representations of the residual lifetime and the inactivity time of systems with such failure-dependent components are considered. Stochastic comparisons of differently structured systems are obtained and properties of the weights in the mixture representations are examined. Furthermore, corresponding representations of the residual lifetime and the inactivity time of a system given the additional information about a previous failure time are derived.

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Section: Mixture Representations Using Additional Information About Amentioning

confidence: 72%

Dynamic Signatures of Coherent Systems Based on Sequential Order Statistics

Burkschat¹,

Navarro²

2013

J. Appl. Probab.

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“…, X * n:n | X * i:n ≤ y < X * i+1:n ) for sequential order statistics. Related recent results in settings of generalized order statistics can be found in Xie and Hu (2008), Balakrishnan et al (2009), Burkschat and Lenz (2009), and Hashemi et al (2010). Here we give some arguments for the univariate relation, i.e.…”

Section: Mixture Representations Using Additional Information About Amentioning

confidence: 84%

Dynamic Signatures of Coherent Systems Based on Sequential Order Statistics

Burkschat

Navarro

2013

Journal of Applied Probability

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“…These dynamic probabilities are then used for obtaining a mixture representation for the residual lifetime of a repairable system. As pointed out in [14,[22][23][24] , there is a close connection between the minimal repair process and record process. The present paper explores some applications of the residual lives of record values in the analysis of a repairable system.…”

Section: Introductionmentioning

confidence: 92%

“…where T(i) denotes the time until the ith failure of the system. It should be mentioned that the minimal repair times have the same joint distribution as record values based on F as well as epoch times of a non-homogeneous Poisson process (NHPP); see [22][23][24]. Hence, the survival function of T(i), for i ⩾ 1, is given by (see p. 496 of [25] or theorem 1 of [5])…”

Section: Model Description and Some Basic Definitionsmentioning

confidence: 99%

Mixture representation for the residual lifetime of a repairable system

Chahkandi

Ahmadi

2017

Appl Stoch Models Bus & Ind

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In this paper, we consider a repairable system in which two types of failures can occur on each failure. One is a minor failure that can be corrected with minimal repair, whereas the other type is a catastrophic failure that destroys the system. The total number of failures until the catastrophic failure is a positive random variable with a given probability vector. It is assumed that there is some partial information about the failure status of the system, and then various properties of the conditional probability of the system failure are studied. Mixture representations of the reliability function for the system in terms of the reliability function of the residual lifetimes of record values are obtained. Some stochastic properties of the conditional probabilities and the residual lifetimes of two systems are finally discussed.failures by minimal repairs, and by system lifetime, we mean the time until a catastrophic failure in the system. The aging properties of the system, under the condition that the system can be repaired (N − 1) times and the Nth failure destroys the system, has been studied in [16]. In this paper, we consider the situation when one may have some partial information about the system lifetime, i.e., the time until the catastrophic failure, and we are then interested in finding the dynamic

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Minimal repair under a step-stress test

Cited by 18 publications

References 30 publications

Dynamic Signatures of Coherent Systems Based on Sequential Order Statistics

Dynamic Signatures of Coherent Systems Based on Sequential Order Statistics

Dynamic Signatures of Coherent Systems Based on Sequential Order Statistics

Mixture representation for the residual lifetime of a repairable system

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