A stress-strength structural reliability model was proposed with a stochastic strength aging deterioration process. In structural engineering,the deterioration of structure's strength should be the total of the de...A stress-strength structural reliability model was proposed with a stochastic strength aging deterioration process. In structural engineering,the deterioration of structure's strength should be the total of the deterioration owing to continual wear, fatigue,corrosion,etc.,and the abrupt deterioration as a result of randomly variable loads. The deterioration of structure's strength should be influenced by both the internal deterioration owing to direct wear and the external deterioration due to randomly variable loads.Meanwhile,the load process was given as Poisson square wave process. The reliability was derived using stress-strength interference theory. In particular,the reliability was also given when random variables followed the normal distribution.展开更多
In reliability analysis,the stress-strength model is often used to describe the life of a component which has a random strength(X)and is subjected to a random stress(Y).In this paper,we considered the problem of estim...In reliability analysis,the stress-strength model is often used to describe the life of a component which has a random strength(X)and is subjected to a random stress(Y).In this paper,we considered the problem of estimating the reliability𝑅𝑅=P[Y<X]when the distributions of both stress and strength are independent and follow exponentiated Pareto distribution.The maximum likelihood estimator of the stress strength reliability is calculated under simple random sample,ranked set sampling and median ranked set sampling methods.Four different reliability estimators under median ranked set sampling are derived.Two estimators are obtained when both strength and stress have an odd or an even set size.The two other estimators are obtained when the strength has an odd size and the stress has an even set size and vice versa.The performances of the suggested estimators are compared with their competitors under simple random sample via a simulation study.The simulation study revealed that the stress strength reliability estimates based on ranked set sampling and median ranked set sampling are more efficient than their competitors via simple random sample.In general,the stress strength reliability estimates based on median ranked set sampling are smaller than the corresponding estimates under ranked set sampling and simple random sample methods.Keywords:Stress-Strength model,ranked set sampling,median ranked set sampling,maximum likelihood estimation,mean square error.corresponding estimates under ranked set sampling and simple random sample methods.展开更多
Stress-strength model is a basic and important tool for reliability analysis.There are few methods to assess the confidence limit of interference reliability when the distribution parameters of stress and strength are...Stress-strength model is a basic and important tool for reliability analysis.There are few methods to assess the confidence limit of interference reliability when the distribution parameters of stress and strength are all unknown.A new assessment method of interference reliability is proposed and the estimates of the distribution parameters are accordingly given.The lower confidence limit of interference reliability with given confidence can be obtained with the method even though the parameters are all unknown.Simulation studies and an engineering application are conducted to validate the method,which suggest that the method provides precise estimates even for sample size of approximately.展开更多
In practical engineering,sometimes the probability density functions( PDFs) of stress and strength can not be exactly determined,or only limited experiment data are available. In these cases,the traditional stress-str...In practical engineering,sometimes the probability density functions( PDFs) of stress and strength can not be exactly determined,or only limited experiment data are available. In these cases,the traditional stress-strength interference( SSI) model based on classical probabilistic approach can not be used to evaluate reliabilities of components. To solve this issue, the traditional universal generating function( UGF) is introduced and then it is extended to represent the discrete interval-valued random variable.Based on the extended UGF,an improved discrete interval-valued SSI model is proposed, which has higher calculation precision compared with the existing methods. Finally,an illustrative case is given to demonstrate the validity of the proposed model.展开更多
The reliability of a system is discussed when the strength of the system and the stress imposed on it are independent and non-identical exponentiated Pareto distributed random variables with progressively censored sch...The reliability of a system is discussed when the strength of the system and the stress imposed on it are independent and non-identical exponentiated Pareto distributed random variables with progressively censored scheme.Different interval estimations are proposed.The interval estimations obtained are exact,approximate and bootstrap confidence intervals.Different methods and the corresponding confidence intervals are compared using Monte-Carlo simulations.Simulation results show that the confidence intervals(CIs)of exact and approximate methods are really better than those of the bootstrap method.展开更多
A method for estimating the component reliability is proposed when the probability density functions of stress and strength can not be exactly determined. For two groups of finite experimental data about the stress an...A method for estimating the component reliability is proposed when the probability density functions of stress and strength can not be exactly determined. For two groups of finite experimental data about the stress and strength, an interval statistics method is introduced. The processed results are formulated as two interval-valued random variables and are graphically represented component reliability are proposed based on the by using two histograms. The lower and upper bounds of universal generating function method and are calculated by solving two discrete stress-strength interference models. The graphical calculations of the proposed reliability bounds are presented through a numerical example and the confidence of the proposed reliability bounds is discussed to demonstrate the validity of the proposed method. It is showed that the proposed reliability bounds can undoubtedly bracket the real reliability value. The proposed method extends the exciting universal generating function method and can give an interval estimation of component reliability in the case of lake of sufficient experimental data. An application example is given to illustrate the proposed method展开更多
The conventional stress-strength interference（SSI） model is a basic model for reliability analysis of mechanical components. In this model, the component reliability is defined as the probability of the strength bei...The conventional stress-strength interference（SSI） model is a basic model for reliability analysis of mechanical components. In this model, the component reliability is defined as the probability of the strength being larger than the stress, where the component stress is generally represented by a single random variable（RV）. But for a component under multi-operating conditions, its reliability can not be calculated directly by using the SSI model. The problem arises from that the stress on a component under multi-operating conditions can not be described by a single RV properly. Current research concerning the SSI model mainly focuses on the calculation of the static or dynamic reliability of the component under single operation condition. To evaluate the component reliability under multi-operating conditions, this paper uses multiple discrete RVs based on the actual stress range of the component firstly. These discrete RVs have identical possible values and different corresponding probability value, which are used to represent the multi-operating conditions of the component. Then the component reliability under each operating condition is calculated, respectively, by employing the discrete SSI model and the universal generating function technique, and from this the discrete SSI model under multi-operating conditions is proposed. Finally the proposed model is applied to evaluate the reliability of a transmission component of the decelerator installed in an aeroengine. The reliability of this component during taking-off, cruising and landing phases of an aircraft are calculated, respectively. With this model, a basic method for reliability analysis of the component under complex load condition is provided, and the application range of the conventional SSI model is extended.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
Many mechanical systems have the characteristics of multiple failure modes and complex failure mech- anisms. On the basis of stress-strength interference （SSI） model, this paper takes the mechanical system with comm...Many mechanical systems have the characteristics of multiple failure modes and complex failure mech- anisms. On the basis of stress-strength interference （SSI） model, this paper takes the mechanical system with common cause failure （CCF） as the research object. The relationship between the stress distribution and the strength distribution is studied, and the failures of components are independent of each other under the determin- istic stress. Then, the concept of conditional reliability is introduced to build the system reliability models under the action of one-stress and multi-stress for both series and parallel systems. Finally, the corresponding properties of the DrODosed methods are discussed to show their advantages.展开更多
In this paper,the statistical inference for system stress-strength reliability with bounded strength is discussed.When the stress and strength variables follow the three-parameter Exponentiated-Weibull distributions w...In this paper,the statistical inference for system stress-strength reliability with bounded strength is discussed.When the stress and strength variables follow the three-parameter Exponentiated-Weibull distributions with unequal scale and shape parameters,the maximum likelihood estimator(MLE)and bootstrap-p confidence interval for system reliability are derived.In addition,combining the score equations which are got by taking the first derivative of the log-likelihood function with respect to the model parameters,the modified generalized pivotal quantity for the system reliability is obtained.After that,two point estimators and a modified generalized confidence interval based on the modified generalized pivotal quantity for the system reliability are derived.Monte Carlo simulations are performed to compare the performances of the proposed point estimators and confidence intervals.Finally,a real data analysis is provided to illustrate the proposed procedures.展开更多
The stress-strength model is widely applied in reliability. Observations are often subject to right censoring due to some practical limitations. In such circumstances, the statistical inference for the stress-strength...The stress-strength model is widely applied in reliability. Observations are often subject to right censoring due to some practical limitations. In such circumstances, the statistical inference for the stress-strength model is demanding, although lacking. We propose a nonparametric method for the inference of the stress-strength model when the observations are subject to right censoring. The asymptotic properties are also established. The practical utility of the proposed method is assessed through both simulated and real data sets.展开更多
基金Natural Science Foundation Project of Fujian Province,China(No.2013J01004)
文摘A stress-strength structural reliability model was proposed with a stochastic strength aging deterioration process. In structural engineering,the deterioration of structure's strength should be the total of the deterioration owing to continual wear, fatigue,corrosion,etc.,and the abrupt deterioration as a result of randomly variable loads. The deterioration of structure's strength should be influenced by both the internal deterioration owing to direct wear and the external deterioration due to randomly variable loads.Meanwhile,the load process was given as Poisson square wave process. The reliability was derived using stress-strength interference theory. In particular,the reliability was also given when random variables followed the normal distribution.
文摘In reliability analysis,the stress-strength model is often used to describe the life of a component which has a random strength(X)and is subjected to a random stress(Y).In this paper,we considered the problem of estimating the reliability𝑅𝑅=P[Y<X]when the distributions of both stress and strength are independent and follow exponentiated Pareto distribution.The maximum likelihood estimator of the stress strength reliability is calculated under simple random sample,ranked set sampling and median ranked set sampling methods.Four different reliability estimators under median ranked set sampling are derived.Two estimators are obtained when both strength and stress have an odd or an even set size.The two other estimators are obtained when the strength has an odd size and the stress has an even set size and vice versa.The performances of the suggested estimators are compared with their competitors under simple random sample via a simulation study.The simulation study revealed that the stress strength reliability estimates based on ranked set sampling and median ranked set sampling are more efficient than their competitors via simple random sample.In general,the stress strength reliability estimates based on median ranked set sampling are smaller than the corresponding estimates under ranked set sampling and simple random sample methods.Keywords:Stress-Strength model,ranked set sampling,median ranked set sampling,maximum likelihood estimation,mean square error.corresponding estimates under ranked set sampling and simple random sample methods.
文摘Stress-strength model is a basic and important tool for reliability analysis.There are few methods to assess the confidence limit of interference reliability when the distribution parameters of stress and strength are all unknown.A new assessment method of interference reliability is proposed and the estimates of the distribution parameters are accordingly given.The lower confidence limit of interference reliability with given confidence can be obtained with the method even though the parameters are all unknown.Simulation studies and an engineering application are conducted to validate the method,which suggest that the method provides precise estimates even for sample size of approximately.
基金National Natural Science Foundation of China(No.51265025)
文摘In practical engineering,sometimes the probability density functions( PDFs) of stress and strength can not be exactly determined,or only limited experiment data are available. In these cases,the traditional stress-strength interference( SSI) model based on classical probabilistic approach can not be used to evaluate reliabilities of components. To solve this issue, the traditional universal generating function( UGF) is introduced and then it is extended to represent the discrete interval-valued random variable.Based on the extended UGF,an improved discrete interval-valued SSI model is proposed, which has higher calculation precision compared with the existing methods. Finally,an illustrative case is given to demonstrate the validity of the proposed model.
基金Natural Science Foundation of Guangdong Province,China(No.2018A030313829)Characteristic Innovation Projects of Ordinary Universities of Guangdong Province,China(No.2019KTSCX202)+1 种基金Higher Education Teaching Reform Project of Guangdong Province,China(No.2019625)Zhaoqing Educational Development Research Institute Project,China(No.ZQJYY2019033)。
文摘The reliability of a system is discussed when the strength of the system and the stress imposed on it are independent and non-identical exponentiated Pareto distributed random variables with progressively censored scheme.Different interval estimations are proposed.The interval estimations obtained are exact,approximate and bootstrap confidence intervals.Different methods and the corresponding confidence intervals are compared using Monte-Carlo simulations.Simulation results show that the confidence intervals(CIs)of exact and approximate methods are really better than those of the bootstrap method.
基金supported by the Foundation of Hunan Provincial Natural Science of China(13JJ6095,2015JJ2015)the Key Project of Science and Technology Program of Changsha,China(ZD1601010)
文摘A method for estimating the component reliability is proposed when the probability density functions of stress and strength can not be exactly determined. For two groups of finite experimental data about the stress and strength, an interval statistics method is introduced. The processed results are formulated as two interval-valued random variables and are graphically represented component reliability are proposed based on the by using two histograms. The lower and upper bounds of universal generating function method and are calculated by solving two discrete stress-strength interference models. The graphical calculations of the proposed reliability bounds are presented through a numerical example and the confidence of the proposed reliability bounds is discussed to demonstrate the validity of the proposed method. It is showed that the proposed reliability bounds can undoubtedly bracket the real reliability value. The proposed method extends the exciting universal generating function method and can give an interval estimation of component reliability in the case of lake of sufficient experimental data. An application example is given to illustrate the proposed method
基金supported by National Hi-tech Research and Development Program of China (863 Program, Grant No. 2007AA04Z403)Sichuan Provincial Key Technologies R&D Program of China(Grant No. 07GG012- 002)+1 种基金Gansu Provincial Basal Research Fund of the Higher Education Institutions of China (Grant No. GCJ 2009019)Research Fund of Lanzhou University of Technology of China(Grant No. BS02200903)
文摘The conventional stress-strength interference（SSI） model is a basic model for reliability analysis of mechanical components. In this model, the component reliability is defined as the probability of the strength being larger than the stress, where the component stress is generally represented by a single random variable（RV）. But for a component under multi-operating conditions, its reliability can not be calculated directly by using the SSI model. The problem arises from that the stress on a component under multi-operating conditions can not be described by a single RV properly. Current research concerning the SSI model mainly focuses on the calculation of the static or dynamic reliability of the component under single operation condition. To evaluate the component reliability under multi-operating conditions, this paper uses multiple discrete RVs based on the actual stress range of the component firstly. These discrete RVs have identical possible values and different corresponding probability value, which are used to represent the multi-operating conditions of the component. Then the component reliability under each operating condition is calculated, respectively, by employing the discrete SSI model and the universal generating function technique, and from this the discrete SSI model under multi-operating conditions is proposed. Finally the proposed model is applied to evaluate the reliability of a transmission component of the decelerator installed in an aeroengine. The reliability of this component during taking-off, cruising and landing phases of an aircraft are calculated, respectively. With this model, a basic method for reliability analysis of the component under complex load condition is provided, and the application range of the conventional SSI model is extended.
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.
基金the National Natural Science Foundation of China(Nos.71771186 and 71471147)the 111 Project(No.B13044)the Basic Research Foundation of Northwestern Polytechnical University(No.3102014JCS05013)
文摘Many mechanical systems have the characteristics of multiple failure modes and complex failure mech- anisms. On the basis of stress-strength interference （SSI） model, this paper takes the mechanical system with common cause failure （CCF） as the research object. The relationship between the stress distribution and the strength distribution is studied, and the failures of components are independent of each other under the determin- istic stress. Then, the concept of conditional reliability is introduced to build the system reliability models under the action of one-stress and multi-stress for both series and parallel systems. Finally, the corresponding properties of the DrODosed methods are discussed to show their advantages.
基金supported by the National Natural Science Foundation of China under Grant Nos.12101475,12101476,11901134,12061091the Soft Science Project of Xi’an under Grant No.22RKYJ0065+1 种基金the Natural Science Basic Research Program of Shaanxi under Grant Nos.2021JQ-186,2020JQ-285the Fundamental Research Funds for the Central Universities under Grant Nos.XJS210603,JGYB2222。
文摘In this paper,the statistical inference for system stress-strength reliability with bounded strength is discussed.When the stress and strength variables follow the three-parameter Exponentiated-Weibull distributions with unequal scale and shape parameters,the maximum likelihood estimator(MLE)and bootstrap-p confidence interval for system reliability are derived.In addition,combining the score equations which are got by taking the first derivative of the log-likelihood function with respect to the model parameters,the modified generalized pivotal quantity for the system reliability is obtained.After that,two point estimators and a modified generalized confidence interval based on the modified generalized pivotal quantity for the system reliability are derived.Monte Carlo simulations are performed to compare the performances of the proposed point estimators and confidence intervals.Finally,a real data analysis is provided to illustrate the proposed procedures.
基金Supported by the National Natural Science Foundation of China(11301545,11401341,11326087)the Fundamental Research Fund for the Central Universities(31541311216)+2 种基金Scientific Research Fund of Fujian Education Department(JA13301)Qingyang Regional Technology Cooperation Planning Project(KH201304)Gansu Education Science "twelfth five-year" Planning Project(GS[2013]GHB1097)
文摘The stress-strength model is widely applied in reliability. Observations are often subject to right censoring due to some practical limitations. In such circumstances, the statistical inference for the stress-strength model is demanding, although lacking. We propose a nonparametric method for the inference of the stress-strength model when the observations are subject to right censoring. The asymptotic properties are also established. The practical utility of the proposed method is assessed through both simulated and real data sets.
