Load-sharing Parallel System Research Articles

Reliability analysis of load-sharing parallel systems considering equivalent strength degradation

In this paper, a new reliability method for load-sharing parallel systems with dependent components that share the workload equally before and after some components have failed is studied. In the working process of a load-sharing parallel system, after the failure of some components, the surviving components share the original system workload with higher components loads. The states of all the components are dependent. The failure behavior of a component impacts the strength degradation process of the remaining working components. For a load-sharing parallel system, one component works the whole system works, which means the component with the largest initial strength works, the whole system works. Firstly, we use the equivalent strength degradation theory to get the remaining strength of the component with the largest initial strength after some components fail. Then, the stress-strength interference model will be used to calculate the reliability after some components fail. Finally, the proposed method is illustrated by a numerical example and verified by the Monte Carlo simulation method.

Estimation of parameters for load-sharing parallel systems under exponential Pareto distribution

This article deals with the estimation of parameters for the load-sharing parallel system when the underlying distribution of component lifetime is exponential Pareto. The appropriate iterative method is used to get the parameter estimators. And the asymptotic distribution of the proposed maximum likelihood estimator is presented. For the model simplified, the maximum likelihood and best asymptotic unbiased estimators of parameters are obtained. Moreover, the confidence intervals for the parameters are constructed using the parameter bootstrap technique. In the end, some appropriate simulation methods and an example are used to substantiate the proposed methods.

Reliability Analysis for Load-Sharing Parallel Systems with No Failure of Components

Conventional reliability analysis of load-sharing parallel systems is mainly based on the assumption that there is failure of components. When a component fails, the load redistributes among the remaining surviving components. But sometimes there is no failure of components during the usage of a load-sharing parallel system. When there is no failure of components, working load is dispatched among components, which means the load on each component is almost the same during the whole working process. The degradation process of each component is also almost the same. The reliability analysis of a load-sharing parallel system with no component fails can be simplified to the reliability analysis of a component. In this paper, three cases are studied. First, based on stress-strength interference model, estimation of component reliability with load application times is generated, which considered the nonlinear fatigue damage model. Then, Poisson process is used to describe reliability changed with time. Third, the reliability is studied when the working load is not constant but changed with time or load application times. Some examples are used to illustrate the application of these models, and the Monte Carlo simulation method is used as standard to verify the proposed models.

On stochastic behaviors of load-sharing parallel systems

This paper mainly investigates a general load-sharing parallel system having two units. First, we construct some comparisons among a load standby system, a warm standby system, a hot standby system and a cold standby system. Moreover, some stochastic comparisons between the load-sharing parallel system and one of its two components are obtained in the sense of the usual stochastic order. Finally, the residual life of this system and its properties are examined.

On Bayesian reliability estimation of a 1-out-of-k load sharing system model of modified Burr-III distribution

This article deals with classical and Bayesian estimation of the parameters of a 1-out-of-k load-sharing parallel system model in which each component’s lifetime follows modified Burr-III distribution. In the classical set up, the maximum likelihood estimates of the load-share parameters, system reliability and hazard rate functions with their bias, standard errors (SEs), average absolute bias (AABias) and width of the confidence interval along with coverage probability are obtained. Besides, two bootstrap confidence intervals for the parameters of the model are also obtained. Further, by assuming both gamma and non-informative priors for the unknown parameters, Bayes estimates of the parameters, system reliability and hazard rate functions with their bias, SEs, AABias and width of the Bayes credible interval along with coverage probability ( $$C_{p}$$ ) are obtained. We have performed a simulation study in order to compare the proposed Bayes estimators with the maximum likelihood estimators. Finally, we analyze one real data set to illustrate the results derived.

MCMC Estimation of Multi-component Load-Sharing System Model and Its Application

In this study, we consider a multi-component load-sharing parallel system model and analyze the load-sharing tendency among the system’s components. The failure time distribution of each component is assumed as Modified Weibull. The maximum-likelihood estimators along with their standard errors of the load-share parameters are computed. The asymptotic and two bootstrap confidence intervals for the parameters are also constructed. Furthermore, Bayesian estimation is carried out by assuming gamma and non-informative priors of the unknown parameters. Markov chain Monte Carlo simulation techniques such as Gibbs sampler and Metropolis–Hasting algorithm have been implemented to obtain Bayes estimates and highest posterior density credible intervals. For highlighting the theoretical developments, a simulation study is conducted. The application of the proposed system model is illustrated by analyzing two real data sets exhibiting load-sharing tendencies.

Stochastic properties and parameter estimation for a general load-sharing system

ABSTRACTWe study here a general load-sharing parallel system in which the lifetimes of the components of the system are arbitrary continuous random variables. The system functions if at least one component in the system functions and the surviving unit shares the whole load. Some sufficient conditions are obtained for the usual stochastic order between two different load-sharing systems. We then consider the optimal allocation problem of one load standby in a series system with two independent components. Finally, the maximum likelihood estimation of the parameters for some specific systems is discussed.

Reliability Evaluation of a Load-sharing Parallel System with Failure Dependence

In a parallel structure load-sharing system, the failure rate of the operating components will usually increase, due to the additional loading induced by the other components' failure. Hence failure dependency exists among components. To quantify the failure dependency, a dependence function is introduced. Under the assumptions that the repair time distributions of components are arbitrary and life times are exponential distributions whose failure rates vary with the number of operating components, a new load-sharing parallel system with failure dependency is proposed. To model the stochastic behavior of the system, the Semi-Markov process induced by it is given. The Semi-Markov kernel associated with the process is also presented. The availability and the time to the first system failure are obtained by employing Markov renewal theory. A numerical example is presented to illustrate the results obtained in the paper. The impact of the failure dependence on the system is also considered.

Inferential statistics on the dynamic system model with time-dependent failure-rate

This study focuses on the classical and Bayesian analysis of a k-components load-sharing parallel system in which components have time-dependent failure rates. In the classical set up, the maximum likelihood estimates of the load-share parameters with their standard errors (SEs) are obtained. (1−γ) 100% simultaneous and two bootstrap confidence intervals for the parameters and system reliability and hazard functions have been constructed. Further, on recognizing the fact that life-testing experiments are very time consuming, the parameters involved in the failure time distribution of the system are expected to follow some random variations. Therefore, Bayes estimates along with their posterior SEs of the parameters and system reliability and hazard functions are obtained by assuming gamma and Jeffrey's priors of the unknown parameters. Markov chain Monte Carlo technique such as Gibbs sampler has been used to obtain Bayes estimates and highest posterior density credible intervals.

Load-sharing system model and its application to the real data set

This study deals with the classical and Bayesian estimation of the parameters of a k-components load-sharing parallel system model in which each component's lifetime follows Lindley distribution. Initially, the failure rate of each of the k components in the system is h(t,θ1) until the first component failure. However, upon the first failure within the system, the failure rates of the remaining (k−1) surviving components change to h(t,θ2) and remain the same until next failure. After second failure, the failure rates of (k−2) surviving components change to h(t,θ3) and finally when the (k−1)th component fails, the failure rate of the last surviving component becomes h(t,θk). In classical set up, the maximum likelihood estimates of the load share parameters, system reliability and hazard rate functions along with their standard errors are computed. 100×(1−γ)% confidence intervals and two bootstrap confidence intervals for the parameters have also been constructed. Further, by assuming Jeffrey's invariant and gamma priors of the unknown parameters, Bayes estimates along with their posterior standard errors and highest posterior density credible intervals of the parameters are obtained. Markov Chain Monte Carlo technique such as Metropolis–Hastings algorithm has been utilized to generate draws from the posterior densities of the parameters.

Analyzing the dynamic system model with discrete failure time distribution

The present study deals with the method of estimation of the parameters of k-components load-sharing parallel system model in which each component’s failure time distribution is assumed to be geometric. The maximum likelihood estimates of the load-share parameters with their standard errors are obtained. (1 − γ) 100% joint, Bonferroni simultaneous and two bootstrap confidence intervals for the parameters have been constructed. Further, recognizing the fact that life testing experiments are time consuming, it seems realistic to consider the load-share parameters to be random variable. Therefore, Bayes estimates along with their standard errors of the parameters are obtained by assuming Jeffrey’s invariant and gamma priors for the unknown parameters. Since, Bayes estimators can not be found in closed form expressions, Tierney and Kadane’s approximation method have been used to compute Bayes estimates and standard errors of the parameters. Markov Chain Monte Carlo technique such as Gibbs sampler is also used to obtain Bayes estimates and highest posterior density credible intervals of the load-share parameters. Metropolis–Hastings algorithm is used to generate samples from the posterior distributions of the unknown parameters.

A classical and Bayesian estimation of a [formula omitted]-components load-sharing parallel system

The present study proposes the classical and Bayesian treatment to the estimation problem of parameters of a k -components load-sharing parallel system in which some of the components follow a constant failure-rate and the remaining follow a linearly increasing failure-rate. In the classical setup, the maximum likelihood estimates of the load-share parameters with their variances are obtained. ( 1 − γ ) 100 % individual, simultaneous, Bonferroni simultaneous and two bootstrap confidence intervals for the parameters have been constructed. Further, on recognizing the fact that life testing experiments are very time consuming, the parameters involved in the failure time distributions of the system are expected to follow some random variations. Therefore, Bayes estimates along with their posterior variances of the parameters are obtained by assuming gamma and Jeffrey’s invariant priors. Markov Chain Monte Carlo techniques such as a Gibbs sampler have also been used to obtain the Bayes estimates and highest posterior density credible intervals when all the parameters follow gamma priors.

Damage Equivalent Method of Fatigue Reliability Analysis of Load-Sharing Parallel System

As for load-sharing parallel system like multi-engine system and wire cable, dependence-failure must occur due to load redistributing, so the component life distributions changed. After the analysis of the disadvantage of failure probability equivalent principle and the transformation of equivalent working time of different life distribution based on damage equivalent principle, the parallel system reliability model applying full probability formula is established. The established reliability model provides a new method for reliability analysis of load-sharing parallel system whose component life follows any distribution.

Reliability analysis for a repairable parallel system with time-varying failure rates

To solve a real problem: how to calculate the reliability of a system with time-varying failure rates in industry systems, this paper studies a model for the load-sharing parallel system with time-varying failure rates, and obtains calculating formulas of reliability and availability of the system by solving differential equations. In this paper, the failure rates are expressed in polynomial configuration. The constant, linear and Weibull failure rate are in their special form. The polynomial failure rates provide flexibility in modeling the practical time-varying failure rates.