This research article is based on a study of optimal frequency to the repairable system due to the failure finding interval to maximize as well as minimize the availability of some components devices. We studied toget...This research article is based on a study of optimal frequency to the repairable system due to the failure finding interval to maximize as well as minimize the availability of some components devices. We studied together maintenance and corrective actions that carried out item of failure and periodic failure finding designed to check whether a system is still working. The model is proved as well as useful application in detecting the problem related to finding failure tasks of different scheme devices by maximization. The model formulated and the numerical application to the relevant mathematical model have been discussed to demonstrate the article quality. Therefore based on probability analytic development, the optimal maintenance policy is then obtained as solution of an optimization problem in which the maintenance cost rate is the objective function and the risk of corrective maintenance is the constraint function. Finally, the solution to the optimal device in the considered development model has been well adjusted due to derivation to the experimental observation rather than theory which will be taken into consideration in the next applied practical design research related and the system device provided that, the proactive device agreed with using the exponential distribution to the survive distribution function which can not be considered as valid.展开更多
This paper deals with a cold standby repairman who can do extra work in idle time. The repairable system with two identical units and one authors are devoted to studying the unique existence and exponential stability ...This paper deals with a cold standby repairman who can do extra work in idle time. The repairable system with two identical units and one authors are devoted to studying the unique existence and exponential stability of the system solution. C0-semigroup theory is used to prove the existence of a unique nonnegative time-dependent solution of the system. Then by using the theory of resolvent positive operator, the authors derive that dynamic solution of the system exponentially converges to its steady-state one which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Some reliability indices of the system are discussed with a different method from traditional one. The authors also make a profit analysis to determine the optimal service time outside the system to maximize the system profit.展开更多
Compared with the classical Markov repairable system, the Markov repairable system with stochastic regimes switching introduced in the paper provides a more realistic description of the practical system. The system ca...Compared with the classical Markov repairable system, the Markov repairable system with stochastic regimes switching introduced in the paper provides a more realistic description of the practical system. The system can be used to model the dynamics of a repairable system whose performance regimes switch according to the external conditions. For example, to satisfy the demand variation that is typical for the power and communication systems and reduce the cost, these systems usually adjust their operating regimes. The transition rate matrices under distinct operating regimes are assumed to be different and the sojourn times in distinct regimes are governed by a finite state Markov chain. By using the theory of Markov process, Ion channel theory, and Laplace transforms, the up time of the system are studied. A numerical example is given to illustrate the obtained results. The effect of sojourn times in distinct regimes on the availability and the up time are also discussed in the numerical example.展开更多
The new model for parallel repairable system is introduced, and it is based on the practice problems of maintenance and the idea of Ion-Channel modeling. In the new model, repair times that are sufficiently short (le...The new model for parallel repairable system is introduced, and it is based on the practice problems of maintenance and the idea of Ion-Channel modeling. In the new model, repair times that are sufficiently short (less than some critical value) do not result in system failure, and such a repair interval is omitted from the downtime record. Usually, the underlying process is Markov process if the durations of working and repair time have the negative-exponential distributions, but the new system has not the Markov properties, which is worth to study. The reliability indexes such as instantaneous availability and steady-state availabilities for the new system are given through probability analysis. A numerical example is given to illustrate the results.展开更多
A two-stage directed Semi-Markov repairable network system is presented in this paper to model the performance of many transmission systems, such as power or oil transmission network, water or gas supply network, etc....A two-stage directed Semi-Markov repairable network system is presented in this paper to model the performance of many transmission systems, such as power or oil transmission network, water or gas supply network, etc. The availability of the system is discussed by using Markov renewal theory, Laplace transform and probability analysis methods. A numerical example is given to illustrate the results obtained in the paper.展开更多
The availability equivalence factors of a general repairable parallel-series system are discussed in this paper considering the availability function of the system. The system components are assumed to be repairable a...The availability equivalence factors of a general repairable parallel-series system are discussed in this paper considering the availability function of the system. The system components are assumed to be repairable and independent but not identical. The life and repair times of the system components are exponentially distributed with different parameters. Two types of availability equivalent factors of the system are derived. The results derived in this paper generalize those given in the literature. A numerical example is introduced to illustrate how the idea of this work can be applied.展开更多
The optimal replacement model for the repairable queueing system con-sisting of single electrical equipment of automatic steel rolling is studied. Assumingthat the equipment after repair is not “as goed as new” , by...The optimal replacement model for the repairable queueing system con-sisting of single electrical equipment of automatic steel rolling is studied. Assumingthat the equipment after repair is not “as goed as new” , by using geometric pro-cess, we take the n展开更多
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,...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.展开更多
Spares inventory configuration optimization is an effective way to improve readiness and reduce life cycle cost of equipment.Through analyzing two-echelon spares support system,the METRIC model basic theory was used.A...Spares inventory configuration optimization is an effective way to improve readiness and reduce life cycle cost of equipment.Through analyzing two-echelon spares support system,the METRIC model basic theory was used.An inventory configuration optimization model of two-echelon spares support system was proposed which took the spares expected shortfall as the object and made the minimum repairable parts expected shortfall instead of the maximum spares supportability as the objective function.Marginal efficiency analysis algorithm was applied to optimizing the spares configuration and generating a rational spares inventory configuration.Finally,several examples are given to verify the model.展开更多
This paper considers a two–unit same cold standby repairable system with a replaceable repair facility and delay repair .The failure time of unit is assumed to follow exponential distribution , and the repair time an...This paper considers a two–unit same cold standby repairable system with a replaceable repair facility and delay repair .The failure time of unit is assumed to follow exponential distribution , and the repair time and delay time of failed unit are assumed to follow arbitrary distributions , whereas the failure and replacement time distributions of the repair facility are exponential and arbitrary . By using the Markov renewal process theory, some primary reliability quantities of the system are obtained.展开更多
The failed components of repairable systems are replaced with spare parts that may have different failure distributions from those of the components that have failed. The spare parts may be either the same as new, bet...The failed components of repairable systems are replaced with spare parts that may have different failure distributions from those of the components that have failed. The spare parts may be either the same as new, better than new, or worse than new. This is the reality in maintenance engineering. Repair with better spare parts is defined as "super repair". The failure distributions of the spare parts affect the availability of the components and their systems. A novel model is proposed to describe the availability of repairable systems across their operating time, at the level of their components, on the assumption that the failed components are immediately replaced. The model functions with arbitrary failure distributions of spare parts. It can be used to compute the availability of components and systems not only under perfect and imperfect repair but also under super repair.展开更多
We investigate a series-parallel repairable system consisting of three-unit with multiple vacations of a repairman. By using C0-semigroup theory of linear operators in the functional analysis, we prove that the system...We investigate a series-parallel repairable system consisting of three-unit with multiple vacations of a repairman. By using C0-semigroup theory of linear operators in the functional analysis, we prove that the system is well-posed and has a unique positive dynamic solution.展开更多
A engineering system is usually repairable, and failure process of a repairable by a failure point process. The power law model is a commonly used approach to model syst the em is often described failure point process...A engineering system is usually repairable, and failure process of a repairable by a failure point process. The power law model is a commonly used approach to model syst the em is often described failure point process. This paper introduces the concept and model for the failure process of repairable system. The method of parameter estimation is developed, and failure observations are fitted into a power-law model by using the least square method. Two applications of the pressent model are discussed according to the practical failure data of the central cooling system of a nuclear power plant. One application is determining the optimal overhaul time, and the other is evaluating the quality of maintenance. This paper provides references for the overhaul decision making and maintenance quality evaluation in reality.展开更多
For a repairable redundant system consisting of two same components with exponential lifetime and general repair time distribution, the probability densities of the system in some state at time t were determined b...For a repairable redundant system consisting of two same components with exponential lifetime and general repair time distribution, the probability densities of the system in some state at time t were determined by a group of ordinary and partial differential equations, called density evolution equations. It was proved that the time dependent solution of the density evolution equations uniquely exists and strongly converges to its steady state density solution by a semi group method. In this proof, it is not necessary to suppose that the repair rate function is bounded. The technique of the proof is valuable for many density evolution equations.展开更多
In this paper, reliability of some typical non-Markov repairable systems, including series systems, m-out-of- n or majority vote systems, and n : m cross-strapping standby redundant systems with general repair-time di...In this paper, reliability of some typical non-Markov repairable systems, including series systems, m-out-of- n or majority vote systems, and n : m cross-strapping standby redundant systems with general repair-time distribution, are studied by applying the generalized Markov renewal process (GMRP). The stochastic behavior of the typical systems is analyzed here. Formulas for mean time to first system failure, MTBF, MTTR, and availability are then developed.展开更多
A two-state system was taken as an example to show the method that we derived for analyzing the instantaneous reliability index,which was an important issue in the field of reliability.The paper first described the sy...A two-state system was taken as an example to show the method that we derived for analyzing the instantaneous reliability index,which was an important issue in the field of reliability.The paper first described the system as an abstract Cauchy problem by choosing suitable operators and state spaces.Then,with the TrotterKato theorem and strong continuous semi-group theorem,the method of solving the instantaneous reliability index of the repairable system was constructed.The convergence of the method was also proved in theory in this paper.To show the effectiveness of this method,some numerical examples were given at the end of the paper.展开更多
Gnedenko, the father of the modern Reliability Theory, first derived some fundamental properties of reliable systems following rigid deductive logic. This paper shares the deductive method and infers four principal pr...Gnedenko, the father of the modern Reliability Theory, first derived some fundamental properties of reliable systems following rigid deductive logic. This paper shares the deductive method and infers four principal properties of repairable/maintainable systems using the Boltzmann-like entropy. In particular we calculate the reparability function and next discuss the physical meanings of the formal results. Lastly we comment on the broad range of applications and researches which can relate to this study.展开更多
We study a series-parallel repairable system consisting of three units with multiple vacations of a repairman. We first show that all points on the imaginary axis except zero belong to the resolvent set of the operato...We study a series-parallel repairable system consisting of three units with multiple vacations of a repairman. We first show that all points on the imaginary axis except zero belong to the resolvent set of the operator and zero is an eigenvalue of the operator, and then we prove that the semigroup generated by the operator is irreducible. By combining these results with our previous result we deduce that the dynamic solution of the system converges strongly to its steady-state solution. Thus we obtain asymptotic stability of the dynamic solution of the system.展开更多
The work deals with the development of analytical model of multichannel technical queuing system with unreliable servers and input memory where server failure flows and incoming request flows comply with Poissonian la...The work deals with the development of analytical model of multichannel technical queuing system with unreliable servers and input memory where server failure flows and incoming request flows comply with Poissonian laws, while the flows of failed facilities repairs and flows of incoming requests comply with exponential laws of probability distribution. Random process of system change-over is a Markovian process with continuous time and discrete states. Relations binding basic parameters and output characteristics of the system indicated are obtained as probabilities of system staying in the given moment in one of the possible states. The proposed model is the most generalized compared to some models known in literature which could be considered as special cases of the considered model.展开更多
In this paper, we systematically discuss the basic concepts of grey theory, particularly the grey differential equation and its mathematical foundation, which is essentially unknown in the reliability engineering comm...In this paper, we systematically discuss the basic concepts of grey theory, particularly the grey differential equation and its mathematical foundation, which is essentially unknown in the reliability engineering community. Accordingly, we propose a small-sample based approach to estimate repair improvement effects by partitioning system stopping times into intrinsic functioning times and repair improvement times. An industrial data set is used for illustrative purposes in a stepwise manner.展开更多
文摘This research article is based on a study of optimal frequency to the repairable system due to the failure finding interval to maximize as well as minimize the availability of some components devices. We studied together maintenance and corrective actions that carried out item of failure and periodic failure finding designed to check whether a system is still working. The model is proved as well as useful application in detecting the problem related to finding failure tasks of different scheme devices by maximization. The model formulated and the numerical application to the relevant mathematical model have been discussed to demonstrate the article quality. Therefore based on probability analytic development, the optimal maintenance policy is then obtained as solution of an optimization problem in which the maintenance cost rate is the objective function and the risk of corrective maintenance is the constraint function. Finally, the solution to the optimal device in the considered development model has been well adjusted due to derivation to the experimental observation rather than theory which will be taken into consideration in the next applied practical design research related and the system device provided that, the proactive device agreed with using the exponential distribution to the survive distribution function which can not be considered as valid.
基金supported by the National Natural Science Foundation of China under Grant No.11201007
文摘This paper deals with a cold standby repairman who can do extra work in idle time. The repairable system with two identical units and one authors are devoted to studying the unique existence and exponential stability of the system solution. C0-semigroup theory is used to prove the existence of a unique nonnegative time-dependent solution of the system. Then by using the theory of resolvent positive operator, the authors derive that dynamic solution of the system exponentially converges to its steady-state one which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Some reliability indices of the system are discussed with a different method from traditional one. The authors also make a profit analysis to determine the optimal service time outside the system to maximize the system profit.
基金supported by the National Natural Science Foundation of China (71071020 60705036)Beijing Excellent Doctoral Dissertation Instructor Project of Humanities and Social Sciences(yb20091000701)
文摘Compared with the classical Markov repairable system, the Markov repairable system with stochastic regimes switching introduced in the paper provides a more realistic description of the practical system. The system can be used to model the dynamics of a repairable system whose performance regimes switch according to the external conditions. For example, to satisfy the demand variation that is typical for the power and communication systems and reduce the cost, these systems usually adjust their operating regimes. The transition rate matrices under distinct operating regimes are assumed to be different and the sojourn times in distinct regimes are governed by a finite state Markov chain. By using the theory of Markov process, Ion channel theory, and Laplace transforms, the up time of the system are studied. A numerical example is given to illustrate the obtained results. The effect of sojourn times in distinct regimes on the availability and the up time are also discussed in the numerical example.
基金Sponsored bythe National Natural Science Foundation of China(70671009)the Postgraduate Science and Innovation Project of Beijing Instituteof Technology (GC200818)
文摘The new model for parallel repairable system is introduced, and it is based on the practice problems of maintenance and the idea of Ion-Channel modeling. In the new model, repair times that are sufficiently short (less than some critical value) do not result in system failure, and such a repair interval is omitted from the downtime record. Usually, the underlying process is Markov process if the durations of working and repair time have the negative-exponential distributions, but the new system has not the Markov properties, which is worth to study. The reliability indexes such as instantaneous availability and steady-state availabilities for the new system are given through probability analysis. A numerical example is given to illustrate the results.
文摘A two-stage directed Semi-Markov repairable network system is presented in this paper to model the performance of many transmission systems, such as power or oil transmission network, water or gas supply network, etc. The availability of the system is discussed by using Markov renewal theory, Laplace transform and probability analysis methods. A numerical example is given to illustrate the results obtained in the paper.
文摘The availability equivalence factors of a general repairable parallel-series system are discussed in this paper considering the availability function of the system. The system components are assumed to be repairable and independent but not identical. The life and repair times of the system components are exponentially distributed with different parameters. Two types of availability equivalent factors of the system are derived. The results derived in this paper generalize those given in the literature. A numerical example is introduced to illustrate how the idea of this work can be applied.
文摘The optimal replacement model for the repairable queueing system con-sisting of single electrical equipment of automatic steel rolling is studied. Assumingthat the equipment after repair is not “as goed as new” , by using geometric pro-cess, we take the n
文摘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.
文摘Spares inventory configuration optimization is an effective way to improve readiness and reduce life cycle cost of equipment.Through analyzing two-echelon spares support system,the METRIC model basic theory was used.An inventory configuration optimization model of two-echelon spares support system was proposed which took the spares expected shortfall as the object and made the minimum repairable parts expected shortfall instead of the maximum spares supportability as the objective function.Marginal efficiency analysis algorithm was applied to optimizing the spares configuration and generating a rational spares inventory configuration.Finally,several examples are given to verify the model.
基金Supported by the National Education Ministry for Chinese University Excellent Teachers (No.Y02012011001001) and the Academic and Technical Leader Training Foundation of Sichuan Province (No.Y02001011001003)
文摘This paper considers a two–unit same cold standby repairable system with a replaceable repair facility and delay repair .The failure time of unit is assumed to follow exponential distribution , and the repair time and delay time of failed unit are assumed to follow arbitrary distributions , whereas the failure and replacement time distributions of the repair facility are exponential and arbitrary . By using the Markov renewal process theory, some primary reliability quantities of the system are obtained.
文摘The failed components of repairable systems are replaced with spare parts that may have different failure distributions from those of the components that have failed. The spare parts may be either the same as new, better than new, or worse than new. This is the reality in maintenance engineering. Repair with better spare parts is defined as "super repair". The failure distributions of the spare parts affect the availability of the components and their systems. A novel model is proposed to describe the availability of repairable systems across their operating time, at the level of their components, on the assumption that the failed components are immediately replaced. The model functions with arbitrary failure distributions of spare parts. It can be used to compute the availability of components and systems not only under perfect and imperfect repair but also under super repair.
文摘We investigate a series-parallel repairable system consisting of three-unit with multiple vacations of a repairman. By using C0-semigroup theory of linear operators in the functional analysis, we prove that the system is well-posed and has a unique positive dynamic solution.
基金supported by the National Natural Science Foundation of China(71771029)
文摘A engineering system is usually repairable, and failure process of a repairable by a failure point process. The power law model is a commonly used approach to model syst the em is often described failure point process. This paper introduces the concept and model for the failure process of repairable system. The method of parameter estimation is developed, and failure observations are fitted into a power-law model by using the least square method. Two applications of the pressent model are discussed according to the practical failure data of the central cooling system of a nuclear power plant. One application is determining the optimal overhaul time, and the other is evaluating the quality of maintenance. This paper provides references for the overhaul decision making and maintenance quality evaluation in reality.
文摘For a repairable redundant system consisting of two same components with exponential lifetime and general repair time distribution, the probability densities of the system in some state at time t were determined by a group of ordinary and partial differential equations, called density evolution equations. It was proved that the time dependent solution of the density evolution equations uniquely exists and strongly converges to its steady state density solution by a semi group method. In this proof, it is not necessary to suppose that the repair rate function is bounded. The technique of the proof is valuable for many density evolution equations.
基金This work is supported by Openning Laboratory of Complex System Control,Institute of Automation, Academia Sinica
文摘In this paper, reliability of some typical non-Markov repairable systems, including series systems, m-out-of- n or majority vote systems, and n : m cross-strapping standby redundant systems with general repair-time distribution, are studied by applying the generalized Markov renewal process (GMRP). The stochastic behavior of the typical systems is analyzed here. Formulas for mean time to first system failure, MTBF, MTTR, and availability are then developed.
基金Joint Funds of the National Natural Science Foundation of China(NSAF)(No.U1430125)
文摘A two-state system was taken as an example to show the method that we derived for analyzing the instantaneous reliability index,which was an important issue in the field of reliability.The paper first described the system as an abstract Cauchy problem by choosing suitable operators and state spaces.Then,with the TrotterKato theorem and strong continuous semi-group theorem,the method of solving the instantaneous reliability index of the repairable system was constructed.The convergence of the method was also proved in theory in this paper.To show the effectiveness of this method,some numerical examples were given at the end of the paper.
文摘Gnedenko, the father of the modern Reliability Theory, first derived some fundamental properties of reliable systems following rigid deductive logic. This paper shares the deductive method and infers four principal properties of repairable/maintainable systems using the Boltzmann-like entropy. In particular we calculate the reparability function and next discuss the physical meanings of the formal results. Lastly we comment on the broad range of applications and researches which can relate to this study.
文摘We study a series-parallel repairable system consisting of three units with multiple vacations of a repairman. We first show that all points on the imaginary axis except zero belong to the resolvent set of the operator and zero is an eigenvalue of the operator, and then we prove that the semigroup generated by the operator is irreducible. By combining these results with our previous result we deduce that the dynamic solution of the system converges strongly to its steady-state solution. Thus we obtain asymptotic stability of the dynamic solution of the system.
文摘The work deals with the development of analytical model of multichannel technical queuing system with unreliable servers and input memory where server failure flows and incoming request flows comply with Poissonian laws, while the flows of failed facilities repairs and flows of incoming requests comply with exponential laws of probability distribution. Random process of system change-over is a Markovian process with continuous time and discrete states. Relations binding basic parameters and output characteristics of the system indicated are obtained as probabilities of system staying in the given moment in one of the possible states. The proposed model is the most generalized compared to some models known in literature which could be considered as special cases of the considered model.
文摘In this paper, we systematically discuss the basic concepts of grey theory, particularly the grey differential equation and its mathematical foundation, which is essentially unknown in the reliability engineering community. Accordingly, we propose a small-sample based approach to estimate repair improvement effects by partitioning system stopping times into intrinsic functioning times and repair improvement times. An industrial data set is used for illustrative purposes in a stepwise manner.