Discrete-event system simulation technology is used to analyze distribution system reliability in this paper. A simulation model, including entity state models, system state models, state transition models, reliabilit...Discrete-event system simulation technology is used to analyze distribution system reliability in this paper. A simulation model, including entity state models, system state models, state transition models, reliability criterion model, is established. ‘Next happen event’ is taken as impulse principle of simulator clock to determine the sequence of random event occurrence dynamically. The results show this method is feasible.展开更多
A general version of the inverted exponential distribution is introduced, studied and analyzed. This generalization depends on the method of Marshall-Olkin to extend a family of distributions. Some statistical and rel...A general version of the inverted exponential distribution is introduced, studied and analyzed. This generalization depends on the method of Marshall-Olkin to extend a family of distributions. Some statistical and reliability properties of this family are studied. In addition, numerical estimation of the maximum likelihood estimate(MLE) parameters are discussed in details. As an application, some real data sets are analyzed and it is observed that the presented family provides a better fit than some other known distributions.展开更多
In modeling reliability data,the exponential distribution is commonly used due to its simplicity.For estimating the parameter of the exponential distribution,classical estimators including maximum likelihood estimator...In modeling reliability data,the exponential distribution is commonly used due to its simplicity.For estimating the parameter of the exponential distribution,classical estimators including maximum likelihood estimator represent the most commonly used method and are well known to be efficient.However,the maximum likelihood estimator is highly sensitive in the presence of contamination or outliers.In this study,a robust and efficient estimator of the exponential distribution parameter was proposed based on the probability integral transform statistic.To examine the robustness of this new estimator,asymptotic variance,breakdown point,and gross error sensitivity were derived.This new estimator offers reasonable protection against outliers besides being simple to compute.Furthermore,a simulation study was conducted to compare the performance of this new estimator with the maximum likelihood estimator,weighted likelihood estimator,and M-scale estimator in the presence of outliers.Finally,a statistical analysis of three reliability data sets was conducted to demonstrate the performance of the proposed estimator.展开更多
Small sample size problem is one of the main problems that heavy numerical control(NC) machine tools encounter in their reliability assessment. In order to deal with the small sample size problem, many indirect reliab...Small sample size problem is one of the main problems that heavy numerical control(NC) machine tools encounter in their reliability assessment. In order to deal with the small sample size problem, many indirect reliability data such as reliability data of similar products, expert opinion, and engineers' experience are used in reliability assessment. However, the existing mathematical theories cannot simultaneously process the above reliability data of multiple types, and thus imprecise probability theory is introduced. Imprecise probability theory can simultaneously process multiple reliability data by quantifying multiple uncertainties(stochastic uncertainty,fuzzy uncertainty, epistemic uncertainty, etc.) together. Although imprecise probability theory has so many advantages, the existing natural extension models are complex and the computation result is imprecise. Therefore,they need some improvement for the better application of reliability engineering. This paper proposes an improved imprecise reliability assessment method by introducing empirical probability distributions to natural extension model, and the improved natural extension model is applied to the reliability assessment of heavy NC machine tool spindle to illustrate its effectiveness.展开更多
A modified Bayesian reliability assessment method of binomial components was proposed by fusing prior information of similar products.The traditional Bayesian method usually directly used all the prior data,ignoring t...A modified Bayesian reliability assessment method of binomial components was proposed by fusing prior information of similar products.The traditional Bayesian method usually directly used all the prior data,ignoring the differences between them,which might decrease the credibility level of reliability evaluation and result in data submergence.To solve the problem,a revised approach was derived to calculate groups of prior data's quantitative credibility,used for weighted data fusion.Then inheritance factor was introduced to build a mixed beta distribution to illustrate the innovation of new products.However,in many cases,inheritance factor was determined by Chi-square test that could not give out exact result with respect to rare failures.To make the model more precise,Barnard's exact test was suggested being used to calculate the inheritance factor.A numerical example is given to demonstrate that the modified method is successful and rational,while the classical method is too conservative and the traditional Bayesian method is too risky.展开更多
With the uncertainties related to operating conditions,in-service non-destructive testing(NDT) measurements and material properties considered in the structural integrity assessment,probabilistic analysis based on t...With the uncertainties related to operating conditions,in-service non-destructive testing(NDT) measurements and material properties considered in the structural integrity assessment,probabilistic analysis based on the failure assessment diagram(FAD) approach has recently become an important concern.However,the point density revealing the probabilistic distribution characteristics of the assessment points is usually ignored.To obtain more detailed and direct knowledge from the reliability analysis,an improved probabilistic fracture mechanics(PFM) assessment method is proposed.By integrating 2D kernel density estimation(KDE) technology into the traditional probabilistic assessment,the probabilistic density of the randomly distributed assessment points is visualized in the assessment diagram.Moreover,a modified interval sensitivity analysis is implemented and compared with probabilistic sensitivity analysis.The improved reliability analysis method is applied to the assessment of a high pressure pipe containing an axial internal semi-elliptical surface crack.The results indicate that these two methods can give consistent sensitivities of input parameters,but the interval sensitivity analysis is computationally more efficient.Meanwhile,the point density distribution and its contour are plotted in the FAD,thereby better revealing the characteristics of PFM assessment.This study provides a powerful tool for the reliability analysis of critical structures.展开更多
A Bayesian sequential testing method is proposed to evaluate system reliability index with reliability growth during development.The method develops a reliability growth model of repairable systems for failure censore...A Bayesian sequential testing method is proposed to evaluate system reliability index with reliability growth during development.The method develops a reliability growth model of repairable systems for failure censored test,and figures out the approach to determine the prior distribution of the system failure rate by applying the reliability growth model to incorporate the multistage test data collected from system development.Furthermore,the procedure for the Bayesian sequential testing is derived for the failure rate of the exponential life system,which enables the decision to terminate or continue development test.Finally,a numerical example is given to illustrate the efficiency of the proposed model and procedure.展开更多
As a bladder accumulator is a high reliable and long life component in a hydraulic system,its cost is high and it takes a lot of time to test its reliability,therefore,a reliability test with small sample is performed...As a bladder accumulator is a high reliable and long life component in a hydraulic system,its cost is high and it takes a lot of time to test its reliability,therefore,a reliability test with small sample is performed,and no failure data is obtained using the method of fixed time truncation. In the case of Weibull distribution,a life reliability model of bladder energy storage is established by Bayesian method using the optimal confidence intervals method,a model of one-sided lower confidence intervals of the reliability and one-sided lower confidence intervals model of the reliability life are established. Results of experiments show that the evaluation method of no failure data under Weibull distribution is a good way to evaluate the reliability of the accumulator,which is convenient for engineering application,and the reliability of the accumulator has theoretical and practical significance.展开更多
Taking into account the whole system structure and the component reliability estimation uncertainty, a system reliability estimation method based on probability and statistical theory for distributed monitoring system...Taking into account the whole system structure and the component reliability estimation uncertainty, a system reliability estimation method based on probability and statistical theory for distributed monitoring systems is presented. The variance and confidence intervals of the system reliability estimation are obtained by expressing system reliability as a linear sum of products of higher order moments of component reliability estimates when the number of component or system survivals obeys binomial distribution. The eigenfunction of binomial distribution is used to determine the moments of component reliability estimates, and a symbolic matrix which can facilitate the search of explicit system reliability estimates is proposed. Furthermore, a case of application is used to illustrate the procedure, and with the help of this example, various issues such as the applicability of this estimation model, and measures to improve system reliability of monitoring systems are discussed.展开更多
We propose a procedure to obtain accurate confidence intervals for the stress-strength reliability R = P (X > Y) when (X, Y) is a bivariate normal distribution with unknown means and covariance matrix. Our method i...We propose a procedure to obtain accurate confidence intervals for the stress-strength reliability R = P (X > Y) when (X, Y) is a bivariate normal distribution with unknown means and covariance matrix. Our method is more accurate than standard methods as it possesses a third-order distributional accuracy. Simulations studies are provided to show the performance of the proposed method relative to existing ones in terms of coverage probability and average length. An empirical example is given to illustrate its usefulness in practice.展开更多
With the support of the Fundamental Reliability Theoretical Research (FRTR) Foundation of the Quality Control Bureau of Ministry of Astronautics (MOA), PRC, 9 Chinese institutes and universities have worked for years ...With the support of the Fundamental Reliability Theoretical Research (FRTR) Foundation of the Quality Control Bureau of Ministry of Astronautics (MOA), PRC, 9 Chinese institutes and universities have worked for years on reliability statistics problems pending to be solved in space research and development. This paper gives a brief review of our main research results, including (1) Results on Normal Distributions; (2) Results on Weibull Distributions; (3) Results on the Synthesisof System Reliability-Theoretical Method; (4) Results on the Synthesis of System Reliability-Approximation Method: Binomial Distribution, Exponential Distribution, Weibull Distribution, Parallel System, General Cases; (5) Structual Reliability; (6) Zero-Failure Reliability Estimation; (7) Storage Life and Others. All these results can be acquired from the Quality Control Bureau of the Ministry of Aero-Space Industry (MAS).展开更多
Opting to follow the computing-design philosophy that the best way to reduce power consumption and increase energy efficiency is to reduce waste, we propose an architecture with a very simple ready-implementation by u...Opting to follow the computing-design philosophy that the best way to reduce power consumption and increase energy efficiency is to reduce waste, we propose an architecture with a very simple ready-implementation by using an NComputing device that can allow multi-users but only one computer is needed. This intuitively can save energy, space as well as cost. In this paper, we propose a simple and realistic NComputing architecture to study the energy and power-efficient consumption of desktop computer systems by using the NComputing device. We also propose new approaches to estimate the reliability of k-out-of-n systems based on the delta method. The k-out-of-n system consisting of n subsystems works if and only if at least k-of-the-n subsystems work. More specificly, we develop approaches to obtain the reliability estimation for the k-out-of-n systems which is composed of n independent and identically distributed subsystems where each subsystem (or energy-efficient usage application) can be assumed to follow a two-parameter exponential lifetime distribution function. The detailed derivations of reliability estimation of k-out-of-n systems based on the biased-corrected estimator, known as delta method, the uniformly minimum variance unbiased estimate (UMVUE) and maximum likelihood estimate (MLE) are discussed. An energy-management NComputing application is discussed to illustrate the reliability results in terms of the energy consumption usages of a computer system with qua(t-core, 8 GB of RAM, and a GeForce 9800GX-2 graphics card to perform various complex applications. The estimated reliability values of systems based on the UMVUE and the delta method differ only slightly. Often the UMVUE of reliability for a complex system is a lot more difficult to obtain, if not impossible. The delta method seems to be a simple and better approach to obtain the reliability estimation of complex systems. The results of this study also show that, in practice, the NComputing architecture improves both energy cost saving and energy efficient living spaces.展开更多
An important property that any lifetime model should satisfy is scale invariance.In this paper,a new scale-invariant quasi-inverse Lindley(QIL)model is presented and studied.Its basic properties,including moments,quan...An important property that any lifetime model should satisfy is scale invariance.In this paper,a new scale-invariant quasi-inverse Lindley(QIL)model is presented and studied.Its basic properties,including moments,quantiles,skewness,kurtosis,and Lorenz curve,have been investigated.In addition,the well-known dynamic reliability measures,such as failure rate(FR),reversed failure rate(RFR),mean residual life(MRL),mean inactivity time(MIT),quantile residual life(QRL),and quantile inactivity time(QIT)are discussed.The FR function considers the decreasing or upside-down bathtub-shaped,and the MRL and median residual lifetime may have a bathtub-shaped form.The parameters of the model are estimated by applying the maximum likelihood method and the expectation-maximization(EM)algorithm.The EM algorithm is an iterative method suitable for models with a latent variable,for example,when we have mixture or competing risk models.A simulation study is then conducted to examine the consistency and efficiency of the estimators and compare them.The simulation study shows that the EM approach provides a better estimation of the parameters.Finally,the proposed model is fitted to a reliability engineering data set along with some alternatives.The Akaike information criterion(AIC),Kolmogorov-Smirnov(K-S),Cramer-von Mises(CVM),and Anderson Darling(AD)statistics are used to compare the considered models.展开更多
This paper is devoted to study a new generalization of the flexible Weibull with three parameters. This model is referred to as the exponential flexible Weibull extension (EFWE) distribution which exhibits bathtub-sha...This paper is devoted to study a new generalization of the flexible Weibull with three parameters. This model is referred to as the exponential flexible Weibull extension (EFWE) distribution which exhibits bathtub-shaped hazard rate function. Some statistical properties such as the mode, median, the moment, quantile function, the moment generating function and order statistics are discussed. Moreover, the maximum likelihood method for estimating the model parameters and the Fisher’s information matrix is given. Finally, the advantage of the EFWE distribution is concluded by an application using real data.展开更多
In this paper,we consider a system which has k statistically independent and identically distributed strength components and each component is constructed by a pair of statistically dependent elements with doubly type...In this paper,we consider a system which has k statistically independent and identically distributed strength components and each component is constructed by a pair of statistically dependent elements with doubly type-II censored scheme.These elements(X1,Y1),(X2,Y2),…,(Xk,Yk)follow a bivariate Kumaraswamy distribution and each element is exposed to a common random stress T which follows a Kumaraswamy distribution.The system is regarded as operating only if at least s out of k(1≤s≤k)strength variables exceed the random stress.The multicomponent reliability of the system is given by Rs,k=P(at least s of the(Z1,…,Zk)exceed T)where Zi=min(Xi,Yi),i=1,…,k.The Bayes estimates of Rs,k have been developed by using the Markov Chain Monte Carlo methods due to the lack of explicit forms.The uniformly minimum variance unbiased and exact Bayes estimates of Rs,k are obtained analytically when the common second shape parameter is known.The asymptotic confidence interval and the highest probability density credible interval are constructed for Rs,k.The reliability estimators are compared by using the estimated risks through Monte Carlo simulations.展开更多
We present Bayes estimators, highest posterior density (HPD) intervals, and maximum likelihood estimators (MLEs), for the Maxwell failure distribution based on Type II censored data, i.e. using the first r lifetimes f...We present Bayes estimators, highest posterior density (HPD) intervals, and maximum likelihood estimators (MLEs), for the Maxwell failure distribution based on Type II censored data, i.e. using the first r lifetimes from a group of n components under test. Reliability/Hazard function estimates, Bayes predictive distributions and highest posterior density prediction intervals for a future observation are also considered. Two data examples and a Monte Carlo simulation study are used to illustrate the results and to compare the performances of the different methods.展开更多
The lifetime data of products with multiple failure modes which are collected from life testing are often fitted by the mixed Weibull distributions. Since the mixed Weibull distributions contain no less than five para...The lifetime data of products with multiple failure modes which are collected from life testing are often fitted by the mixed Weibull distributions. Since the mixed Weibull distributions contain no less than five parameters,the parameter estimation is difficult and inaccurate. In order to enhance the accuracy,a new method of parameter estimation based on Cuckoo search( CS) is proposed. An optimization model for the mixed Weibull distribution is formulated by minimizing the residual sum of squares. The optimal parameters are searched via CS algorithm. In the case study,the lifetime data come from the life testing of diesel injectors and are fitted by the twocomponent Weibull mixture. Regarding the maximum absolute error and the accumulative absolute error between estimated and observed values as the accuracy index of parameter estimation,the results of four parameter estimation methods that the graphic estimation method,the nonlinear least square method,the optimization method based on particle swarm optimization( PSO) and the proposed method are compared. The result shows that the proposed method is more efficient and more accurate than the other three methods.展开更多
In this paper, we discuss the mixture model of two extreme lower bound distributions. First, some properties we obtain of the model with hazard function are discussed. In addition, the estimates of the unknown paramet...In this paper, we discuss the mixture model of two extreme lower bound distributions. First, some properties we obtain of the model with hazard function are discussed. In addition, the estimates of the unknown parameters via the EM algorithm are obtained. The performance of the findings in the paper is showed by demonstrating some numerical illustrations through Monte Carlo simulation.展开更多
By proportional differentiating cumulative distribution function of normal distribution,the spectroscopy characteristics are found.The characteristic parameters can be extracted directly from the height and position o...By proportional differentiating cumulative distribution function of normal distribution,the spectroscopy characteristics are found.The characteristic parameters can be extracted directly from the height and position of the spectroscopy peaks.On this basis,a new method for determining these parameters of normal distribution is developed.This method can be applied to microelectronics reliability study.展开更多
基金SupportedbyNationalNatureScienceFoundation No .5 0 1770 17
文摘Discrete-event system simulation technology is used to analyze distribution system reliability in this paper. A simulation model, including entity state models, system state models, state transition models, reliability criterion model, is established. ‘Next happen event’ is taken as impulse principle of simulator clock to determine the sequence of random event occurrence dynamically. The results show this method is feasible.
基金supported by the Research Center of the Female Scientific and Medical Colleges,Deanship of Scientific Research,King Saud University
文摘A general version of the inverted exponential distribution is introduced, studied and analyzed. This generalization depends on the method of Marshall-Olkin to extend a family of distributions. Some statistical and reliability properties of this family are studied. In addition, numerical estimation of the maximum likelihood estimate(MLE) parameters are discussed in details. As an application, some real data sets are analyzed and it is observed that the presented family provides a better fit than some other known distributions.
基金This work is supported by the Universiti Kebangsaan Malaysia[Grant Number DIP-2018-038].
文摘In modeling reliability data,the exponential distribution is commonly used due to its simplicity.For estimating the parameter of the exponential distribution,classical estimators including maximum likelihood estimator represent the most commonly used method and are well known to be efficient.However,the maximum likelihood estimator is highly sensitive in the presence of contamination or outliers.In this study,a robust and efficient estimator of the exponential distribution parameter was proposed based on the probability integral transform statistic.To examine the robustness of this new estimator,asymptotic variance,breakdown point,and gross error sensitivity were derived.This new estimator offers reasonable protection against outliers besides being simple to compute.Furthermore,a simulation study was conducted to compare the performance of this new estimator with the maximum likelihood estimator,weighted likelihood estimator,and M-scale estimator in the presence of outliers.Finally,a statistical analysis of three reliability data sets was conducted to demonstrate the performance of the proposed estimator.
基金the National Natural Science Foundation of China(No.51405065)the National Science and Technology Major Project of China(No.2014ZX04014-011)
文摘Small sample size problem is one of the main problems that heavy numerical control(NC) machine tools encounter in their reliability assessment. In order to deal with the small sample size problem, many indirect reliability data such as reliability data of similar products, expert opinion, and engineers' experience are used in reliability assessment. However, the existing mathematical theories cannot simultaneously process the above reliability data of multiple types, and thus imprecise probability theory is introduced. Imprecise probability theory can simultaneously process multiple reliability data by quantifying multiple uncertainties(stochastic uncertainty,fuzzy uncertainty, epistemic uncertainty, etc.) together. Although imprecise probability theory has so many advantages, the existing natural extension models are complex and the computation result is imprecise. Therefore,they need some improvement for the better application of reliability engineering. This paper proposes an improved imprecise reliability assessment method by introducing empirical probability distributions to natural extension model, and the improved natural extension model is applied to the reliability assessment of heavy NC machine tool spindle to illustrate its effectiveness.
基金National Natural Science Foundation of China(No.71371182)
文摘A modified Bayesian reliability assessment method of binomial components was proposed by fusing prior information of similar products.The traditional Bayesian method usually directly used all the prior data,ignoring the differences between them,which might decrease the credibility level of reliability evaluation and result in data submergence.To solve the problem,a revised approach was derived to calculate groups of prior data's quantitative credibility,used for weighted data fusion.Then inheritance factor was introduced to build a mixed beta distribution to illustrate the innovation of new products.However,in many cases,inheritance factor was determined by Chi-square test that could not give out exact result with respect to rare failures.To make the model more precise,Barnard's exact test was suggested being used to calculate the inheritance factor.A numerical example is given to demonstrate that the modified method is successful and rational,while the classical method is too conservative and the traditional Bayesian method is too risky.
基金supported by National Department Public Benefit Research Foundation of China (Grant No. 200810411)
文摘With the uncertainties related to operating conditions,in-service non-destructive testing(NDT) measurements and material properties considered in the structural integrity assessment,probabilistic analysis based on the failure assessment diagram(FAD) approach has recently become an important concern.However,the point density revealing the probabilistic distribution characteristics of the assessment points is usually ignored.To obtain more detailed and direct knowledge from the reliability analysis,an improved probabilistic fracture mechanics(PFM) assessment method is proposed.By integrating 2D kernel density estimation(KDE) technology into the traditional probabilistic assessment,the probabilistic density of the randomly distributed assessment points is visualized in the assessment diagram.Moreover,a modified interval sensitivity analysis is implemented and compared with probabilistic sensitivity analysis.The improved reliability analysis method is applied to the assessment of a high pressure pipe containing an axial internal semi-elliptical surface crack.The results indicate that these two methods can give consistent sensitivities of input parameters,but the interval sensitivity analysis is computationally more efficient.Meanwhile,the point density distribution and its contour are plotted in the FAD,thereby better revealing the characteristics of PFM assessment.This study provides a powerful tool for the reliability analysis of critical structures.
基金supported by the National Natural Science Foundation of China (70571083)the Research Fund for the Doctoral Program of Higher Education of China (20094307110013)
文摘A Bayesian sequential testing method is proposed to evaluate system reliability index with reliability growth during development.The method develops a reliability growth model of repairable systems for failure censored test,and figures out the approach to determine the prior distribution of the system failure rate by applying the reliability growth model to incorporate the multistage test data collected from system development.Furthermore,the procedure for the Bayesian sequential testing is derived for the failure rate of the exponential life system,which enables the decision to terminate or continue development test.Finally,a numerical example is given to illustrate the efficiency of the proposed model and procedure.
基金Supported by the National Natural Science Foundation of China(No.51405424,51675461,11673040)
文摘As a bladder accumulator is a high reliable and long life component in a hydraulic system,its cost is high and it takes a lot of time to test its reliability,therefore,a reliability test with small sample is performed,and no failure data is obtained using the method of fixed time truncation. In the case of Weibull distribution,a life reliability model of bladder energy storage is established by Bayesian method using the optimal confidence intervals method,a model of one-sided lower confidence intervals of the reliability and one-sided lower confidence intervals model of the reliability life are established. Results of experiments show that the evaluation method of no failure data under Weibull distribution is a good way to evaluate the reliability of the accumulator,which is convenient for engineering application,and the reliability of the accumulator has theoretical and practical significance.
基金This project is supported by National Natural Science Foundation of China(No.50335020,No.50205009)Laboratory of Intelligence Manufacturing Technology of Ministry of Education of China(No.J100301).
文摘Taking into account the whole system structure and the component reliability estimation uncertainty, a system reliability estimation method based on probability and statistical theory for distributed monitoring systems is presented. The variance and confidence intervals of the system reliability estimation are obtained by expressing system reliability as a linear sum of products of higher order moments of component reliability estimates when the number of component or system survivals obeys binomial distribution. The eigenfunction of binomial distribution is used to determine the moments of component reliability estimates, and a symbolic matrix which can facilitate the search of explicit system reliability estimates is proposed. Furthermore, a case of application is used to illustrate the procedure, and with the help of this example, various issues such as the applicability of this estimation model, and measures to improve system reliability of monitoring systems are discussed.
文摘We propose a procedure to obtain accurate confidence intervals for the stress-strength reliability R = P (X > Y) when (X, Y) is a bivariate normal distribution with unknown means and covariance matrix. Our method is more accurate than standard methods as it possesses a third-order distributional accuracy. Simulations studies are provided to show the performance of the proposed method relative to existing ones in terms of coverage probability and average length. An empirical example is given to illustrate its usefulness in practice.
文摘With the support of the Fundamental Reliability Theoretical Research (FRTR) Foundation of the Quality Control Bureau of Ministry of Astronautics (MOA), PRC, 9 Chinese institutes and universities have worked for years on reliability statistics problems pending to be solved in space research and development. This paper gives a brief review of our main research results, including (1) Results on Normal Distributions; (2) Results on Weibull Distributions; (3) Results on the Synthesisof System Reliability-Theoretical Method; (4) Results on the Synthesis of System Reliability-Approximation Method: Binomial Distribution, Exponential Distribution, Weibull Distribution, Parallel System, General Cases; (5) Structual Reliability; (6) Zero-Failure Reliability Estimation; (7) Storage Life and Others. All these results can be acquired from the Quality Control Bureau of the Ministry of Aero-Space Industry (MAS).
基金supported by Rutgers CCC Green Computing Initiative
文摘Opting to follow the computing-design philosophy that the best way to reduce power consumption and increase energy efficiency is to reduce waste, we propose an architecture with a very simple ready-implementation by using an NComputing device that can allow multi-users but only one computer is needed. This intuitively can save energy, space as well as cost. In this paper, we propose a simple and realistic NComputing architecture to study the energy and power-efficient consumption of desktop computer systems by using the NComputing device. We also propose new approaches to estimate the reliability of k-out-of-n systems based on the delta method. The k-out-of-n system consisting of n subsystems works if and only if at least k-of-the-n subsystems work. More specificly, we develop approaches to obtain the reliability estimation for the k-out-of-n systems which is composed of n independent and identically distributed subsystems where each subsystem (or energy-efficient usage application) can be assumed to follow a two-parameter exponential lifetime distribution function. The detailed derivations of reliability estimation of k-out-of-n systems based on the biased-corrected estimator, known as delta method, the uniformly minimum variance unbiased estimate (UMVUE) and maximum likelihood estimate (MLE) are discussed. An energy-management NComputing application is discussed to illustrate the reliability results in terms of the energy consumption usages of a computer system with qua(t-core, 8 GB of RAM, and a GeForce 9800GX-2 graphics card to perform various complex applications. The estimated reliability values of systems based on the UMVUE and the delta method differ only slightly. Often the UMVUE of reliability for a complex system is a lot more difficult to obtain, if not impossible. The delta method seems to be a simple and better approach to obtain the reliability estimation of complex systems. The results of this study also show that, in practice, the NComputing architecture improves both energy cost saving and energy efficient living spaces.
基金supported by Researchers Supporting Project Number(RSP-2021/392),King Saud University,Riyadh,Saudi Arabia.
文摘An important property that any lifetime model should satisfy is scale invariance.In this paper,a new scale-invariant quasi-inverse Lindley(QIL)model is presented and studied.Its basic properties,including moments,quantiles,skewness,kurtosis,and Lorenz curve,have been investigated.In addition,the well-known dynamic reliability measures,such as failure rate(FR),reversed failure rate(RFR),mean residual life(MRL),mean inactivity time(MIT),quantile residual life(QRL),and quantile inactivity time(QIT)are discussed.The FR function considers the decreasing or upside-down bathtub-shaped,and the MRL and median residual lifetime may have a bathtub-shaped form.The parameters of the model are estimated by applying the maximum likelihood method and the expectation-maximization(EM)algorithm.The EM algorithm is an iterative method suitable for models with a latent variable,for example,when we have mixture or competing risk models.A simulation study is then conducted to examine the consistency and efficiency of the estimators and compare them.The simulation study shows that the EM approach provides a better estimation of the parameters.Finally,the proposed model is fitted to a reliability engineering data set along with some alternatives.The Akaike information criterion(AIC),Kolmogorov-Smirnov(K-S),Cramer-von Mises(CVM),and Anderson Darling(AD)statistics are used to compare the considered models.
文摘This paper is devoted to study a new generalization of the flexible Weibull with three parameters. This model is referred to as the exponential flexible Weibull extension (EFWE) distribution which exhibits bathtub-shaped hazard rate function. Some statistical properties such as the mode, median, the moment, quantile function, the moment generating function and order statistics are discussed. Moreover, the maximum likelihood method for estimating the model parameters and the Fisher’s information matrix is given. Finally, the advantage of the EFWE distribution is concluded by an application using real data.
基金supported by the Natural Science Foundation of Guangdong(No.2024A1515010983)the project of Guangdong Province General Colleges and Universities with Special Characteristics and Innovations(No.2022KTSCX150)+2 种基金Zhaoqing Science and Technology Innovation Guidance Project(No.2023040317006)Zhaoqing Institute of Education Development Project(No.ZQJYY2023021)Zhaoqing College Quality Project and Teaching Reform Project(No.zlgc202112).
文摘In this paper,we consider a system which has k statistically independent and identically distributed strength components and each component is constructed by a pair of statistically dependent elements with doubly type-II censored scheme.These elements(X1,Y1),(X2,Y2),…,(Xk,Yk)follow a bivariate Kumaraswamy distribution and each element is exposed to a common random stress T which follows a Kumaraswamy distribution.The system is regarded as operating only if at least s out of k(1≤s≤k)strength variables exceed the random stress.The multicomponent reliability of the system is given by Rs,k=P(at least s of the(Z1,…,Zk)exceed T)where Zi=min(Xi,Yi),i=1,…,k.The Bayes estimates of Rs,k have been developed by using the Markov Chain Monte Carlo methods due to the lack of explicit forms.The uniformly minimum variance unbiased and exact Bayes estimates of Rs,k are obtained analytically when the common second shape parameter is known.The asymptotic confidence interval and the highest probability density credible interval are constructed for Rs,k.The reliability estimators are compared by using the estimated risks through Monte Carlo simulations.
文摘We present Bayes estimators, highest posterior density (HPD) intervals, and maximum likelihood estimators (MLEs), for the Maxwell failure distribution based on Type II censored data, i.e. using the first r lifetimes from a group of n components under test. Reliability/Hazard function estimates, Bayes predictive distributions and highest posterior density prediction intervals for a future observation are also considered. Two data examples and a Monte Carlo simulation study are used to illustrate the results and to compare the performances of the different methods.
文摘The lifetime data of products with multiple failure modes which are collected from life testing are often fitted by the mixed Weibull distributions. Since the mixed Weibull distributions contain no less than five parameters,the parameter estimation is difficult and inaccurate. In order to enhance the accuracy,a new method of parameter estimation based on Cuckoo search( CS) is proposed. An optimization model for the mixed Weibull distribution is formulated by minimizing the residual sum of squares. The optimal parameters are searched via CS algorithm. In the case study,the lifetime data come from the life testing of diesel injectors and are fitted by the twocomponent Weibull mixture. Regarding the maximum absolute error and the accumulative absolute error between estimated and observed values as the accuracy index of parameter estimation,the results of four parameter estimation methods that the graphic estimation method,the nonlinear least square method,the optimization method based on particle swarm optimization( PSO) and the proposed method are compared. The result shows that the proposed method is more efficient and more accurate than the other three methods.
文摘In this paper, we discuss the mixture model of two extreme lower bound distributions. First, some properties we obtain of the model with hazard function are discussed. In addition, the estimates of the unknown parameters via the EM algorithm are obtained. The performance of the findings in the paper is showed by demonstrating some numerical illustrations through Monte Carlo simulation.
文摘By proportional differentiating cumulative distribution function of normal distribution,the spectroscopy characteristics are found.The characteristic parameters can be extracted directly from the height and position of the spectroscopy peaks.On this basis,a new method for determining these parameters of normal distribution is developed.This method can be applied to microelectronics reliability study.