In this note, the expectation value of time based on quantum mechanics formalism is derived. It is found that the expectation value of time does not depend on space.
On the basis of strict mathematical description about Failure_Free Period Life Test (FFPLT), the statistical properties of the tests and optimal confidence limit of the parameter are discussed in detail and correspond...On the basis of strict mathematical description about Failure_Free Period Life Test (FFPLT), the statistical properties of the tests and optimal confidence limit of the parameter are discussed in detail and corresponding calculating formulae are found out.展开更多
Provided an algorithm for the distribution search and proves the time complexity of the algorithm. This algorithm uses a mathematical formula to search n elements in the sequence of n elements in O(n)expected time,and...Provided an algorithm for the distribution search and proves the time complexity of the algorithm. This algorithm uses a mathematical formula to search n elements in the sequence of n elements in O(n)expected time,and experimental reesult proves that distribution search is superior to binary search.展开更多
The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximu...The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximum likelihood estimators of the parameters and their confidence intervals are derived. The expected time required to complete the life test under this censoring scheme is investigated. Finally, the numerical examples are given to illustrate some theoretical results by means of Monte-Carlo simulation.展开更多
This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units re...This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units removed at each failure time follows the binomial distribution.The maximum likelihood estimation and the Bayesian estimation are derived.In the meanwhile,through a great quantity of Monte Carlo simulation experiments we have studied different hyperparameters as well as symmetric and asymmetric loss functions in the Bayesian estimation procedure.A real industrial case is presented to justify and illustrate the proposed methods.We also investigate the expected experimentation time and discuss the influence of the parameters on the termination point to complete the censoring test.展开更多
Cuckoo search(CS) has been used successfully for solving global optimization problems.From a theoretical point of view,the convergence of the CS is an important issue.In this paper,convergence analysis of CS was studi...Cuckoo search(CS) has been used successfully for solving global optimization problems.From a theoretical point of view,the convergence of the CS is an important issue.In this paper,convergence analysis of CS was studied.The transition probability characteristics of the population to construct a Markov chain were analyzed.The homogeneity of the Markov chain was derived based on stochastic process theory.Then it was proved to be an absorbing state Markov chain.Consequently,the global convergence of CS was deduced based on conditions of convergence sequence and total probability formula,and the expected convergence time was given.Finally,a series of experiments were conducted.Experimental results were analyzed and it is observed that CS seems to perform better than PSO.展开更多
In water industry, the chlorine is mostly used as a disinfectant agent. The chlorine present in potable water as a disinfectant has been reported to reduce the lifetime of contact polymeric material. This occurs in po...In water industry, the chlorine is mostly used as a disinfectant agent. The chlorine present in potable water as a disinfectant has been reported to reduce the lifetime of contact polymeric material. This occurs in polymer pipes and it is now very common in plumbing and other parts of the drinking water distribution system. For more than 50 years, Polymer & Elastomeric materials have been used ubiquitously in drinking water distribution systems. Polymer & Elastomeric materials have successfully been used in a variety of applications ranging from rubber gaskets, to valves, to hydrants, to fittings. Polymer & Elastomers that degrade more quickly than expected create service problems, make it difficult for utilities to cost efficient plan preventive maintenance programs, and negatively affect customer relations. This review paper gives an insight idea to a reader about the selection of proper polymer & elastomer and predicting its performance in chlorinated water. Also the mechanism of degradation of Polymer & elastomer in chlorine environment and some model of life expectancy of in-service of Polymer & elastomer in various conditions and parameter in chlorinated water were discussed.展开更多
A traffic sensitive spectrum access scheme is proposed to satisfy the traffic load requirement of secondary users （SUs）. In the proposed design, SU only accesses available channels which can meet the traffic demand....A traffic sensitive spectrum access scheme is proposed to satisfy the traffic load requirement of secondary users （SUs）. In the proposed design, SU only accesses available channels which can meet the traffic demand. To achieve this, the expected transmission time （E3W） of the SU is calcu- lated first based on the delivery ratio. Then, the channel idle time is estimated based on the activity of primary users （PUs）. Therefore, available channels with estimated idle time longer than ETr could be chosen. With high probability, the SU can finish transmission on these channels without disruption, thereby satisfying the traffic load demand of the SU. Finally, our method is extended to the multi-channel scenario where each SU can access multiple channels simultaneously. Performance analysis shows that our method satisfies the requirement of SUs while effectively improving the throughput.展开更多
In this paper we research the single machine stochastic JIT scheduling problem subject to the machine breakdowns for preemptive-resume and preemptive-repeat.The objective function of the problem is the sum of squared ...In this paper we research the single machine stochastic JIT scheduling problem subject to the machine breakdowns for preemptive-resume and preemptive-repeat.The objective function of the problem is the sum of squared deviations of the job-expected completion times from the due date.For preemptive-resume,we show that the optimal sequence of the SSDE problem is V-shaped with respect to expected processing times.And a dynamic programming algorithm with the pseudopolynomial time complexity is given.We discuss the difference between the SSDE problem and the ESSD problem and show that the optimal solution of the SSDE problem is a good approximate optimal solution of the ESSD problem,and the optimal solution of the SSDE problem is an optimal solution of the ESSD problem under some conditions.For preemptive-repeat,the stochastic JIT scheduling problem has not been solved since the variances of the completion times cannot be computed.We replace the ESSD problem by the SSDE problem.We show that the optimal sequence of the SSDE problem is V-shaped with respect to the expected occupying times.And a dynamic programming algorithm with the pseudopolynomial time complexity is given.A new thought is advanced for the research of the preemptive-repeat stochastic JIT scheduling problem.展开更多
Recently, Sandia Laboratories developed a neutron scatter camera to detect special nuclear materials. This camera exhibits the following advantages: high efficiency, direction discrimination, neutron-gamma discriminat...Recently, Sandia Laboratories developed a neutron scatter camera to detect special nuclear materials. This camera exhibits the following advantages: high efficiency, direction discrimination, neutron-gamma discrimination ability, and wide field of view. However, using the direct projection method, the angular resolution of this camera is limited by uncertainties in the energies estimated from pulse height and time of flight measurements. In this study, we established an eight-element neutron scatter camera and conducted the experiment with a ^(252)Cf neutron source. The results show that it has an angular resolution better than 8°(1s) and a detection efficiency of approximately 2.6′10-4. Using maximum likelihood expectation maximization method, the image artifact was eliminated, and the angular resolution was improved. We proposed an average scattering angle method to estimate the scattering energy of neutrons and Compton gamma rays. As such, we can obtain a recognizable image and energy spectrum of the source with some degradation of energy and image resolutions. Finally, a newly measured light response function based on the MPD^(-4) device was used for image reconstruction. Although we did not obtain a better result than that of the standard light response function, we have observed the effects of light response function on image reconstruction.展开更多
The In-Parameter-Order （IPO） algorithm is a widely used strategy for the construction of software test suites for combinatorial testing （CT） whose goal is to reveal faults triggered by interactions among parameter...The In-Parameter-Order （IPO） algorithm is a widely used strategy for the construction of software test suites for combinatorial testing （CT） whose goal is to reveal faults triggered by interactions among parameters. Variants of IPO have been shown to produce test suites within reasonable amounts of time that are often not much larger than the smallest test suites known. When an entire test suite is executed, all faults that arise from t-way interactions for some fixed t are surely found. However, when tests are executed one at a time, it is desirable to detect a fault as early as possible so that it can be repaired. The basic IPO strategies of horizontal and vertical growth address test suite size, but not the early detection of faults. In this paper, the growth strategies in IPO are modified to attempt to evenly distribute the values of each parameter across the tests. Together with a reordering strategy that we add, this modification to IPO improves the rate of fault detection dramatically （improved by 31% on average）. Moreover, our modifications always reduce generation time （2 times faster on average） and in some eases also reduce test suite size.展开更多
Aiming at the problem that the asset’s fluctuation influences the borrower’s repayment ability,a loan with a new and flexible repayment method is designed,which depends on the asset value of the borrower.The repayme...Aiming at the problem that the asset’s fluctuation influences the borrower’s repayment ability,a loan with a new and flexible repayment method is designed,which depends on the asset value of the borrower.The repayment method can reduce the loan default probability,but it causes the uncertainty of the pay off time.Because the repayment term is related to the regular repayment amount in this method,a boundary for the regular repayment amount is set up in order to avoid too long repayment term.This will balance the benefit of borrowers and lenders and improve the applicability of this method.By establishing a mathematical model of the residual value of the loan,this model can be transformed into an initial-boundary problem of a partial differential equation.The analytic solution and the expected time to pay off the loan are obtained.Finally,numerical analysis are shown.展开更多
This paper aims to propose ERT （Expected Reaching Time）, a new risk adverse evaluation criterion of finite multiplication processes, and to examine its properties in relation to the dominance criterion. The ERT mean...This paper aims to propose ERT （Expected Reaching Time）, a new risk adverse evaluation criterion of finite multiplication processes, and to examine its properties in relation to the dominance criterion. The ERT means the expected time that takes for an objective valiable to reach a target value. To deal with the environmental risk involved in the process, the expectation maximizing strategy may be the most well known. However, for many cases the dominance strategy rather than the expectation maximizing strategy is adopted and works very well. In this paper we first prove rigorously that minimization of the ERT is equivalent to the dominance criterion in the infinite period. Then we demonstrate by simulation that the ERT gives almost equal evaluation as the dominance criterion even for the finite multiplications, after showing that it is approximately proportional to the logarithm of the target value.展开更多
文摘In this note, the expectation value of time based on quantum mechanics formalism is derived. It is found that the expectation value of time does not depend on space.
文摘On the basis of strict mathematical description about Failure_Free Period Life Test (FFPLT), the statistical properties of the tests and optimal confidence limit of the parameter are discussed in detail and corresponding calculating formulae are found out.
文摘Provided an algorithm for the distribution search and proves the time complexity of the algorithm. This algorithm uses a mathematical formula to search n elements in the sequence of n elements in O(n)expected time,and experimental reesult proves that distribution search is superior to binary search.
基金supported by the National Natural Science Foundation of China(70471057)
文摘The estimation of generalized exponential distribution based on progressive censoring with binomial removals is presented, where the number of units removed at each failure time follows a binomial distribution. Maximum likelihood estimators of the parameters and their confidence intervals are derived. The expected time required to complete the life test under this censoring scheme is investigated. Finally, the numerical examples are given to illustrate some theoretical results by means of Monte-Carlo simulation.
基金supported by the National Statistical Science Research Project of China(2019LZ32)
文摘This paper considers the parameters and reliability characteristics estimation problem of the generalized Rayleigh distribution under progressively Type-Ⅱ censoring with random removals,that is,the number of units removed at each failure time follows the binomial distribution.The maximum likelihood estimation and the Bayesian estimation are derived.In the meanwhile,through a great quantity of Monte Carlo simulation experiments we have studied different hyperparameters as well as symmetric and asymmetric loss functions in the Bayesian estimation procedure.A real industrial case is presented to justify and illustrate the proposed methods.We also investigate the expected experimentation time and discuss the influence of the parameters on the termination point to complete the censoring test.
基金National Natural Science Foundation of China(No.61174065)
文摘Cuckoo search(CS) has been used successfully for solving global optimization problems.From a theoretical point of view,the convergence of the CS is an important issue.In this paper,convergence analysis of CS was studied.The transition probability characteristics of the population to construct a Markov chain were analyzed.The homogeneity of the Markov chain was derived based on stochastic process theory.Then it was proved to be an absorbing state Markov chain.Consequently,the global convergence of CS was deduced based on conditions of convergence sequence and total probability formula,and the expected convergence time was given.Finally,a series of experiments were conducted.Experimental results were analyzed and it is observed that CS seems to perform better than PSO.
文摘In water industry, the chlorine is mostly used as a disinfectant agent. The chlorine present in potable water as a disinfectant has been reported to reduce the lifetime of contact polymeric material. This occurs in polymer pipes and it is now very common in plumbing and other parts of the drinking water distribution system. For more than 50 years, Polymer & Elastomeric materials have been used ubiquitously in drinking water distribution systems. Polymer & Elastomeric materials have successfully been used in a variety of applications ranging from rubber gaskets, to valves, to hydrants, to fittings. Polymer & Elastomers that degrade more quickly than expected create service problems, make it difficult for utilities to cost efficient plan preventive maintenance programs, and negatively affect customer relations. This review paper gives an insight idea to a reader about the selection of proper polymer & elastomer and predicting its performance in chlorinated water. Also the mechanism of degradation of Polymer & elastomer in chlorine environment and some model of life expectancy of in-service of Polymer & elastomer in various conditions and parameter in chlorinated water were discussed.
基金Supported by the National High Technology Research and Development Programme of China(No.2011AA010503)the National Natural Science Foundation of China(No.60903192)
文摘A traffic sensitive spectrum access scheme is proposed to satisfy the traffic load requirement of secondary users （SUs）. In the proposed design, SU only accesses available channels which can meet the traffic demand. To achieve this, the expected transmission time （E3W） of the SU is calcu- lated first based on the delivery ratio. Then, the channel idle time is estimated based on the activity of primary users （PUs）. Therefore, available channels with estimated idle time longer than ETr could be chosen. With high probability, the SU can finish transmission on these channels without disruption, thereby satisfying the traffic load demand of the SU. Finally, our method is extended to the multi-channel scenario where each SU can access multiple channels simultaneously. Performance analysis shows that our method satisfies the requirement of SUs while effectively improving the throughput.
基金the National Natural Science Foundation of China (Grant No.10471096)
文摘In this paper we research the single machine stochastic JIT scheduling problem subject to the machine breakdowns for preemptive-resume and preemptive-repeat.The objective function of the problem is the sum of squared deviations of the job-expected completion times from the due date.For preemptive-resume,we show that the optimal sequence of the SSDE problem is V-shaped with respect to expected processing times.And a dynamic programming algorithm with the pseudopolynomial time complexity is given.We discuss the difference between the SSDE problem and the ESSD problem and show that the optimal solution of the SSDE problem is a good approximate optimal solution of the ESSD problem,and the optimal solution of the SSDE problem is an optimal solution of the ESSD problem under some conditions.For preemptive-repeat,the stochastic JIT scheduling problem has not been solved since the variances of the completion times cannot be computed.We replace the ESSD problem by the SSDE problem.We show that the optimal sequence of the SSDE problem is V-shaped with respect to the expected occupying times.And a dynamic programming algorithm with the pseudopolynomial time complexity is given.A new thought is advanced for the research of the preemptive-repeat stochastic JIT scheduling problem.
基金supported by the National Natural Science Fundation of China(Grant Nos.1110510611375144&11275153)
文摘Recently, Sandia Laboratories developed a neutron scatter camera to detect special nuclear materials. This camera exhibits the following advantages: high efficiency, direction discrimination, neutron-gamma discrimination ability, and wide field of view. However, using the direct projection method, the angular resolution of this camera is limited by uncertainties in the energies estimated from pulse height and time of flight measurements. In this study, we established an eight-element neutron scatter camera and conducted the experiment with a ^(252)Cf neutron source. The results show that it has an angular resolution better than 8°(1s) and a detection efficiency of approximately 2.6′10-4. Using maximum likelihood expectation maximization method, the image artifact was eliminated, and the angular resolution was improved. We proposed an average scattering angle method to estimate the scattering energy of neutrons and Compton gamma rays. As such, we can obtain a recognizable image and energy spectrum of the source with some degradation of energy and image resolutions. Finally, a newly measured light response function based on the MPD^(-4) device was used for image reconstruction. Although we did not obtain a better result than that of the standard light response function, we have observed the effects of light response function on image reconstruction.
基金the National Natural Science Foundation of China under Grant Nos. 61300007 and 61305054, the Fundamental Research Funds for the Central Universities of China under Grant Nos. YWF-15-GJSYS-106 and YWF-14-JSJXY-007, and the Project of the State Key Laboratory of Software Development Environment of China under Grant Nos. SKLSDE-2015ZX-09 and SKLSDE-2014ZX-06.
文摘The In-Parameter-Order （IPO） algorithm is a widely used strategy for the construction of software test suites for combinatorial testing （CT） whose goal is to reveal faults triggered by interactions among parameters. Variants of IPO have been shown to produce test suites within reasonable amounts of time that are often not much larger than the smallest test suites known. When an entire test suite is executed, all faults that arise from t-way interactions for some fixed t are surely found. However, when tests are executed one at a time, it is desirable to detect a fault as early as possible so that it can be repaired. The basic IPO strategies of horizontal and vertical growth address test suite size, but not the early detection of faults. In this paper, the growth strategies in IPO are modified to attempt to evenly distribute the values of each parameter across the tests. Together with a reordering strategy that we add, this modification to IPO improves the rate of fault detection dramatically （improved by 31% on average）. Moreover, our modifications always reduce generation time （2 times faster on average） and in some eases also reduce test suite size.
基金supported by the National Natural Science Foundation of China(No.11671301).
文摘Aiming at the problem that the asset’s fluctuation influences the borrower’s repayment ability,a loan with a new and flexible repayment method is designed,which depends on the asset value of the borrower.The repayment method can reduce the loan default probability,but it causes the uncertainty of the pay off time.Because the repayment term is related to the regular repayment amount in this method,a boundary for the regular repayment amount is set up in order to avoid too long repayment term.This will balance the benefit of borrowers and lenders and improve the applicability of this method.By establishing a mathematical model of the residual value of the loan,this model can be transformed into an initial-boundary problem of a partial differential equation.The analytic solution and the expected time to pay off the loan are obtained.Finally,numerical analysis are shown.
文摘This paper aims to propose ERT （Expected Reaching Time）, a new risk adverse evaluation criterion of finite multiplication processes, and to examine its properties in relation to the dominance criterion. The ERT means the expected time that takes for an objective valiable to reach a target value. To deal with the environmental risk involved in the process, the expectation maximizing strategy may be the most well known. However, for many cases the dominance strategy rather than the expectation maximizing strategy is adopted and works very well. In this paper we first prove rigorously that minimization of the ERT is equivalent to the dominance criterion in the infinite period. Then we demonstrate by simulation that the ERT gives almost equal evaluation as the dominance criterion even for the finite multiplications, after showing that it is approximately proportional to the logarithm of the target value.
