Accelerated Failure Time Models For Load Sharing Systems

Sutar, Santosh S.; Naik‐Nimbalkar, U. V.

doi:10.1109/tr.2014.2313793

Cited by 27 publications

(11 citation statements)

References 37 publications

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“…It is observed that Y 1 is not distributed as Weibull though Y 2 can be taken to be from a Weibull distribution. Nevertheless, Sutur et al analysed this data and confirmed a load share phenomenon, which motivated us to fit our model to the data in Table , which shows the time to failure data for 18 such systems.…”

Section: Illustration: Reliability Of a System With Two Motorsmentioning

confidence: 83%

Reliability modelling incorporating load share and frailty

Asha

Raja

Равишанкер

2017

Appl Stoch Models Bus & Ind

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The stochastic behaviour of lifetimes of a two component system is often primarily influenced by the system structure and by the covariates shared by the components. Any meaningful attempt to model the lifetimes must take into consideration the factors affecting their stochastic behaviour. In particular, for a load share system, we describe a reliability model incorporating both the load share dependence and the effect of observed and unobserved covariates. The model includes a bivariate Weibull to characterize load share, a positive stable distribution to describe frailty, and also incorporates effects of observed covariates.We investigate various interesting reliability properties of this model using cross ratio functions and conditional survivor functions. We implement maximum likelihood estimation of the model parameters and discuss model adequacy and selection. We illustrate our approach using a simulation study. For a real data situation, we demonstrate the superiority of the proposed model that incorporates both load share and frailty effects over competing models that incorporate just one of these effects. An attractive and computationally simple cross-validation technique is introduced to reconfirm the claim. We conclude with a summary and discussion. KEYWORDSbivariate Weibull distribution, load sharing dependence, maximum likelihood estimation, positive stable frailty, proportional hazards model 206

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Section: Illustration: Reliability Of a System With Two Motorsmentioning

confidence: 83%

Reliability modelling incorporating load share and frailty

Asha

Raja

Равишанкер

2017

Appl Stoch Models Bus & Ind

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“…We apply the tests of Section III to a ReliaSoft data set provided in [30], which was discussed in [31], [32], and, more recently, in [33]. The data is shown in Table V and consists of the failure times x (1) i < x (2) i , i = 1, .…”

Section: Real Data Examplementioning

confidence: 99%

Exact Semiparametric Inference and Model Selection for Load-Sharing Systems

Mies

Bedbur

2020

IEEE Trans. Rel.

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As a specific proportional hazard rates model, sequential order statistics can be used to describe the lifetimes of load-sharing systems. Inference for these systems needs to account for small sample sizes, which are prevalent in reliability applications. By exploiting the probabilistic structure of sequential order statistics, we derive exact finite sample inference procedures to test for the load-sharing parameters and for the nonparametrically specified baseline distribution, treating the respective other part as a nuisance quantity. This improves upon previous approaches for the model, which either assume a fully parametric specification or rely on asymptotic results. Simulations show that the tests derived are able to detect deviations from the null hypothesis at small sample sizes. Critical values for a prominent case are tabulated.

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“…with statisticQ =T (1) /T (2) ; cf. Formulas (9) and (10). Note that for s 1 = s 2 , the likelihood-ratio test and the Rao score test are equivalent, sinceΛ andR are both strictly monotone functions of statistic (T (1) +T (2) ) 2 /(T (1)T (2) ); see also Section 3.2.…”

Section: Asymptotic Testsmentioning

confidence: 99%

“…In a proportional hazard rate setup of SOSs, the uncertainty of the model is captured within some baseline cdf or within a finite number of positive model parameters, for which a variety of inferential results Stats 2019, 2 have been derived. Estimators of model parameters or distribution parameters of the baseline cdf of SOSs are provided in, e.g., References [3][4][5][6][7][8][9][10]. Statistical tests for single or vectors of the model or baseline-distribution parameters of SOSs are proposed in References [3,6,7,[11][12][13], which, in particular, allow for model selection in the sense of whether order statistics have to be rejected for modelling in a given situation.…”

Section: Introductionmentioning

confidence: 99%

Testing for Equality of Parameters from Different Load-Sharing Systems

Bedbur

Kamps

2019

Stats

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In reliability, sequential order statistics serve as a model for the component lifetimes of k-out-of-n systems, which are operating as long as k out of n components are operating. In contrast to modelling with order statistics, load-sharing effects and other impacts of failures on the performance of the remaining components may be taken into consideration. Inference for associated load-sharing parameters, as well as for the underlying baseline distribution, is then of particular interest. In a setup of multiple samples of sequential order statistics modelling the component lifetimes of possibly differently structured k-out-of-n systems, we provide exact statistical tests to check for common load-sharing or common baseline-distribution parameters. In the two-sample case, critical values for the corresponding test statistics are tabulated for small sample sizes, and the asymptotic distributions of the test statistics under the null hypotheses are derived. Based on a simulation study, power comparisons are addressed. The proposed tests may be applied to detect significant differences between systems or to decide whether a meta-analysis of the data may be conducted to increase the performance of subsequent inferential procedures.

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Accelerated Failure Time Models For Load Sharing Systems

Cited by 27 publications

References 37 publications

Reliability modelling incorporating load share and frailty

Reliability modelling incorporating load share and frailty

Exact Semiparametric Inference and Model Selection for Load-Sharing Systems

Testing for Equality of Parameters from Different Load-Sharing Systems

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