Order restricted inference for sequential k-out-of-n systems

Beutner, Eric; Kamps, Udo

doi:10.1016/j.jmva.2008.04.014

Cited by 52 publications

(36 citation statements)

References 13 publications

(19 reference statements)

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“…. , n. At time t = 0, we assume that all the n components in a system are working and have independent and identically distributed lifetimes X (1) 1 , X (1) 2 , . .…”

Section: Properties Of Coherent Systems Based On Sosmentioning

confidence: 99%

“…. , X (1) n with distribution F 1 (shortly written as IID ∼ F 1 ). Hence the first component failure is…”

Section: Properties Of Coherent Systems Based On Sosmentioning

confidence: 99%

“…EXAMPLE 3.1: Let us consider a parallel system with two components based on the SOS ∼ F 1 , F 2 . Then, at time t = 0, the lifetimes of the two components X (1) 1 and X (1) 2 are IID with common reliability functionF 1 . Hence, the reliability function of the first failure X *…”

Section: Ordering Properties For K-out-of-n Systems Based On Sosmentioning

confidence: 99%

“…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%

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Coherent systems based on sequential order statistics

Navarro

Burkschat

2011

Naval Research Logistics

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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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“…. , n. At time t = 0, we assume that all the n components in a system are working and have independent and identically distributed lifetimes X (1) 1 , X (1) 2 , . .…”

Section: Properties Of Coherent Systems Based On Sosmentioning

confidence: 99%

“…. , X (1) n with distribution F 1 (shortly written as IID ∼ F 1 ). Hence the first component failure is…”

Section: Properties Of Coherent Systems Based On Sosmentioning

confidence: 99%

Section: Ordering Properties For K-out-of-n Systems Based On Sosmentioning

confidence: 99%

“…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%

See 2 more Smart Citations

Coherent systems based on sequential order statistics

Navarro

Burkschat

2011

Naval Research Logistics

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“…In this setting, a more realistic model results for k-out-of-n system, wherein, upon the failure of a component, an increased stress is put on the remaining active components. For more details on the model and its properties and associated inferential results, one may refer to Cramer and Kamps (1996, 2001a,b, 2003 and Balakrishnan et al (2008).…”

Section: Setting In Terms Of Sequential Order Statisticsmentioning

confidence: 99%

A sequential order statistics approach to step-stress testing

Kamps

Kateri

2010

Ann Inst Stat Math

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For general step-stress experiments with arbitrary baseline distributions, wherein the stress levels change immediately after having observed pre-specified numbers of observations under each stress level, a sequential order statistics model is proposed and associated inferential issues are discussed. Maximum likelihood estimators (MLEs) of the mean lifetimes at different stress levels are derived, and some useful properties of the MLEs are established. Joint MLEs are also derived when an additional location parameter is introduced into the model, and estimation under order restriction of the parameters at different stress levels is finally discussed.

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Step‐Stress Testing with Multiple Samples: The Exponential Case

Kamps¹

2005

Encyclopedia of Statistical Sciences

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Step‐stress models are descriptions of special experiments in the field of accelerated life testing, where the test units are exposed to stress levels that change at intermediate time points during the experiment. The goal is to develop inference for the mean lifetime at each stress level. The time points of stress level change can either be fixed or random. Furthermore, the experiment can be terminated when a certain number of failures is reached or at a pre‐specified time point. These alternative assumptions of the type of the experiment lead to alternative models. Usually the step‐stress models are based on a single experiment. We develop inference for step stress models designed for multiple samples. The stress levels are the same applied to all samples but the duration of exposure under each stress level can vary among the experiments. The likelihood inference is then discussed in detail for the exponential case and different simple step‐stress experiments.

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Order restricted inference for sequential k-out-of-n systems

Cited by 52 publications

References 13 publications

Coherent systems based on sequential order statistics

Coherent systems based on sequential order statistics

A sequential order statistics approach to step-stress testing

Step‐Stress Testing with Multiple Samples: The Exponential Case

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