Sequential order statistics and k-out-of-n systems with sequentially adjusted failure rates

Abstract:The sequential order statistics (SOS) are a good way to model the lifetimes of the components in a system when the failure of a component at time t affects the performance of the working components at this age t. In this article, we study properties of the lifetimes of the coherent systems obtained using SOS. Specifically, we obtain a mixture representation based on the signature of the system. This representation is used to obtain stochastic comparisons. To get these comparisons, we obtain some ordering properties for the SOS, which in this context represent the lifetimes of k-out-of-n systems. In particular, we show that they are not necessarily hazard rate ordered.

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“…General properties and other practical applications of SOS models can be found in Refs. [1,4,[10][11][12]16,19] and in the references therein.…”

Section: Introductionmentioning

confidence: 99%

Coherent systems based on sequential order statistics

Navarro

Burkschat

2011

Naval Research Logistics

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“…A definition of sequential order statistics with a view to the motivation given in the introduction can be found in Cramer and Kamps (1996). As shown in Cramer and Kamps (2003) they can also be defined as follows.…”

Section: Description Of the Modelmentioning

confidence: 99%

Nonparametric inference for sequential k-out-of-n systems

Beutner

2007

Ann Inst Stat Math

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“…One specific variant of classic k-out-of-n testing is the so-called conservative k-out-of-n testing, which is defined in the same way, but testing now continues until either k successful tests are observed or until all n tests have been performed (Hellerstein et al, 2011). In this text, we will assume component tests to be independent; Cramer and Kamps (1996) present a generalization in which the failure rate of the untested components is parametrically adjusted based on the number of preceding failures.…”

Section: Literature Reviewmentioning

confidence: 99%

Sequential Testing of <i>k</i>-out-of-<i>n</i> Systems with Imperfect Tests

et al. 2015

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Abstract. A k-out-of-n system configuration requires that, for the overall system to be functional, at least k out of the total of n components be working. We consider the problem of sequentially testing the components of a k-out-of-n system in order to learn the state of the system, when the tests are costly and when the individual component tests are imperfect, which means that a test can identify a component as working when in reality it is down, and vice versa. Each component is tested at most once. Since tests are imperfect, even when all components are tested the state of the system is not necessarily known with certainty, and so reaching a lower bound on the probability of correctness of the system state is used as a stopping criterion for the inspection.We define different classes of inspection policies and we examine global optimality of each of the classes. We find that a globally optimal policy for diagnosing k-out-of-n systems with imperfect tests can be found in polynomial time when the predictive error probabilities are the same for all the components. Of the three policy classes studied, the dominant policies always contain a global optimum, while elementary policies are compact in representation. The newly introduced class of so-called 'interrupted block-walking' policies combines these merits of global optimality and of compactness.

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Sequential order statistics and k-out-of-n systems with sequentially adjusted failure rates

Abstract: Sequential k-out-of-n-system, sequential order statistics, generalized order statistics, type II censoring, maximum likelihood estimators, extremal quotient, Weibull distributions,

Cited by 122 publications

References 16 publications

Coherent systems based on sequential order statistics

Coherent systems based on sequential order statistics

Nonparametric inference for sequential k-out-of-n systems

Sequential Testing of <i>k</i>-out-of-<i>n</i> Systems with Imperfect Tests

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