Reliability Inference on Composite Dynamic Systems Based on Burr Type-XII Distribution

Jiang, Nan; Tsai, Tzong‐Ru; Lio, Yuhlong; Chen, Ding‐Geng

doi:10.1109/tr.2014.2338251

Cited by 11 publications

(16 citation statements)

References 31 publications

(66 reference statements)

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“…Numerous reliability inference studies regarding CDS have been investigated in literature that is based on SOS samples. Among them, the parametric hazard rate model that was proposed by Balakrishnan, Jiang, Tsai, Lio, and Chen [24] is flexible and simple for obtaining the CI of the baseline survival function of CDS components. Balakrishnan, Jiang, Tsai, Lio, and Chen [24] have presented the analytical statistical properties for the maximum likelihood estimation method.…”

Section: Motivation and Organizationmentioning

confidence: 99%

“…Among them, the parametric hazard rate model that was proposed by Balakrishnan, Jiang, Tsai, Lio, and Chen [24] is flexible and simple for obtaining the CI of the baseline survival function of CDS components. Balakrishnan, Jiang, Tsai, Lio, and Chen [24] have presented the analytical statistical properties for the maximum likelihood estimation method. However, two problems are found when implementing the maximum likelihood estimation method that was proposed by Balakrishnan, Jiang, Tsai, Lio, and Chen [24].…”

Section: Motivation and Organizationmentioning

confidence: 99%

“…Their method is quite generalized and it can be applied for any chosen arbitrary absolutely continuous lifetime distribution. Balakrishnan, Jiang, Tsai, Lio, and Chen [24] proposed inferential methods for the CDSs, in which components in a CDS follow a baseline Burr type XII distribution with a power-trend hazard rate function. Hashempour and Doostparast [23] evaluated the reliability of comparing heterogeneous exponential distributions that are based on independent multiply SOS samples with using the conditionally proportional hazard rate assumption.…”

Section: Introduction 1literature Reviewmentioning

confidence: 99%

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Bayesian Estimation Based on Sequential Order Statistics for Heterogeneous Baseline Gompertz Distributions

2021

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A composite dynamic system (CDS) is composed of multiple components. Each component failure can equally induce higher loading on the surviving components and, hence, enhances the hazard rate of each surviving component. The applications of CDS and the reliability evaluation of CDS has earned more attention in the recent two decades. Because the lifetime quality of components could be inconsistent, the lifetimes of components in the CDS is considered to follow heterogeneous baseline Gompertz distributions in this study. A power-trend hazard rate function is used in order to characterize the hazard rate of the CDS. In order to overcome the difficulty of obtaining reliable estimates of the parameters in the CDS model, the Bayesian estimation method utilizing a hybrid Gibbs sampling and Metropolis-Hasting algorithm to implement the Markov chain Monte Carlo approach is proposed for obtaining the Bayes estimators of the CDS parameters. An intensive simulation study is carried out to evaluate the performance of the proposed estimation method. The simulation results show that the proposed estimation method is reliable in providing reliability evaluation information for the CDS. An example regarding the service system of small electric carts is used for illustration.

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Section: Motivation and Organizationmentioning

confidence: 99%

Section: Motivation and Organizationmentioning

confidence: 99%

Section: Introduction 1literature Reviewmentioning

confidence: 99%

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Bayesian Estimation Based on Sequential Order Statistics for Heterogeneous Baseline Gompertz Distributions

2021

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“…Due to this connection, the theory of order statistics has been utilized to study r-out-of-n systems and to characterize their properties. For detailed discussions on various developments on the theory and applications of order statistics, we refer the interested reader to Arnold et al (1992), Balakrishnan andRao (1998a), (1998b), and David and Nagaraja (2003).…”

Section: Introductionmentioning

confidence: 99%

Univariate and multivariate stochastic orderings of residual lifetimes of live components in sequential (𝑛-𝑟+ 1)-out-of-𝑛 systems

Barmalzan

Haidari

2018

J. Appl. Probab.

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Sequential order statistics can be used to describe the ordered lifetimes of components of a system when the failure of a component may affect the reliability of the remaining components. After a reliability system consisting of n components fails, some of its components may still be alive. In this paper we first establish some univariate stochastic orderings and ageing properties of the residual lifetimes of the live components in a sequential (n-r+1)-out-of-n system. We also obtain a characterizing result for the exponential distribution based on uncorrelated residual lifetimes of live components. Finally, we provide some sufficient conditions for comparing vectors of residual lifetimes of the live components from two sequential (n-r+1)-out-of-n systems. The results established here extend some well-known results in the literature.

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“…The work load adjustment strategy can be generalized to a wider class of infrastructure systems which involves human operators with the ability to make process interventions. Such systems can be regarded as load-sharing systems, since the components share the total work load of the system according to a defined set of load-sharing rules [7][8][9][10]. Reliability modeling of a loadsharing system with managed component degradation is challenging because components in the system are used intermittently.…”

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confidence: 99%

Reliability Modeling of Infrastructure Load-Sharing Systems With Workload Adjustment

Sun

Revie

et al. 2019

IEEE Trans. Rel.

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Motivated by the need to support effective asset management of infrastructure systems, this paper presents a novel reliability model for a load-sharing system where the operator can adjust component work load to balance system degradation. The operator intervention effect, combined with other system complexities, makes modeling reliability interesting and challenging. We first develop cost modeling for a load-sharing system that has experienced operational service at the time of analysis. The system replacement process is modeled as a delayed renewal process for which the expected operational cost of the system is derived. A numerical algorithm is proposed to compute the cost, and the error bound is shown to be of order O(n −1). Next, we extend modeling to consider multiple heterogeneous systems located at different sites within the infrastructure network. Heterogeneities here refer to possible cross-site differences in the operating environments and the operators' actions. When the heterogeneities are observable, we model as covariates; otherwise, we model as random effects. Statistical inference methods are developed for the proposed models. An example using real data from a water utility illustrates the logical model behavior given parameter choices as well as showing how analysis might inform asset management.

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Reliability Inference on Composite Dynamic Systems Based on Burr Type-XII Distribution

Cited by 11 publications

References 31 publications

Bayesian Estimation Based on Sequential Order Statistics for Heterogeneous Baseline Gompertz Distributions

Bayesian Estimation Based on Sequential Order Statistics for Heterogeneous Baseline Gompertz Distributions

Univariate and multivariate stochastic orderings of residual lifetimes of live components in sequential (𝑛-𝑟+ 1)-out-of-𝑛 systems

Reliability Modeling of Infrastructure Load-Sharing Systems With Workload Adjustment

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