Parameter estimation for the reliability of load-sharing systems

Park, Chanseok

doi:10.1080/07408171003670991

Cited by 47 publications

(34 citation statements)

References 30 publications

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“…Therefore, we consider the optimal design problem as follows. (9) To obtain the optimal solution, we need to simplify the objective function. The following result turns out to be helpful.…”

Section: B Long Term Average Cost and The Optimal Design Of Future mentioning

confidence: 99%

A Load Sharing System Reliability Model With Managed Component Degradation

Revie

Walls

2014

IEEE Trans. Rel.

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Motivated by an industrial problem affecting a water utility, we develop a model for a load sharing system where an operator dispatches work load to components in a manner that manages their degradation. We assume degradation is the dominant failure type, and that the system will not be subject to sudden failure due to a shock. By deriving the time to degradation failure of the system, estimates of system probability of failure are generated, and optimal designs can be obtained to minimize the long run average cost of a future system. The model can be used to support asset maintenance and design decisions. Our model is developed under a common set of core assumptions. That is, the operator allocates work to balance the level of the degradation condition of all components to achieve system performance. A system is assumed to be replaced when the cumulative work load reaches some random threshold. We adopt cumulative work load as the measure of total usage because it represents the primary cause of component degradation. We model the cumulative work load of the system as a monotone increasing and stationary stochastic process. The cumulative work load to degradation failure of a component is assumed to be inverse Gaussian distributed. An example, informed by an industry problem, is presented to illustrate the application of the model under different operating scenarios.

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“…Therefore, we consider the optimal design problem as follows. (9) To obtain the optimal solution, we need to simplify the objective function. The following result turns out to be helpful.…”

Section: B Long Term Average Cost and The Optimal Design Of Future mentioning

confidence: 99%

A Load Sharing System Reliability Model With Managed Component Degradation

Revie

Walls

2014

IEEE Trans. Rel.

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“…Kim and Kvam [7] investigated the reliability of the equal load-sharing system whose component failure rates were constant under an unknown load share rule based on system data. Park [8] provided a detailed discussion about the parameter estimation and the evaluation of the reliability of a general load-sharing system model or an equal load-sharing system when the component lifetimes are Weibull-distributed. The procedure provided by Park [8] requires the self-reproducing property, which cannot be true for other lifetime distributions.…”

Section: Introductionmentioning

confidence: 99%

“…Park [8] provided a detailed discussion about the parameter estimation and the evaluation of the reliability of a general load-sharing system model or an equal load-sharing system when the component lifetimes are Weibull-distributed. The procedure provided by Park [8] requires the self-reproducing property, which cannot be true for other lifetime distributions. Park [9] also suggested using an expectation-maximization (EM) algorithm to obtain the maximum-likelihood estimate (MLE) of the reliability of equal load-sharing systems.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2015

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Failure of a component in a composite dynamic system often induces a higher load on surviving components, and increases the hazard rate. Statistical inferential procedures on composite dynamic systems are developed here based on a Burr type-XII distribution with a power-trend hazard rate function. Point estimates of the Burr type-XII parameters, and interval estimates of the baseline survival function are obtained based on the maximum-likelihood estimates, and the Fisher information matrix. A test procedure is presented for examining the relationship between the hazard rate function and the number of failed components. The performance of the proposed method is then evaluated by means of an extensive Monte Carlo simulation study. An example is finally presented for illustrative purpose.Index Terms-Generalized likelihood ratio test, log-likelihood function, observed Fisher information, sequential order statistics.

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“…A lot of papers are devoted to statistical analysis of the load-share parameters [15][16][17][18]. This is only a small part of many papers devoted to load-share models that talks about their importance and applicability.…”

Section: Introductionmentioning

confidence: 99%

A Load-Share Reliability Model under the Changeable Piecewise Smooth Load

Gurov

Utkin

2014

Journal of Quality and Reliability Engineering

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A new load-share reliability model of systems under the changeable load is proposed in the paper. It is assumed that the load is a piecewise smooth function which can be regarded as an extension of the piecewise constant and continuous functions. The condition of the residual lifetime conservation, which means continuity of a cumulative distribution function of time to failure, is accepted in the proposed model. A general algorithm for computing reliability measures is provided. Simple expressions for determining the survivor functions under assumption of the Weibull probability distribution of time to failure are given. Various numerical examples illustrate the proposed model by different forms of the system load and different probability distributions of time to failure.

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Parameter estimation for the reliability of load-sharing systems

Cited by 47 publications

References 30 publications

A Load Sharing System Reliability Model With Managed Component Degradation

A Load Sharing System Reliability Model With Managed Component Degradation

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

A Load-Share Reliability Model under the Changeable Piecewise Smooth Load

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