In this article,mathematical modeling for the evaluation of reliability is studied using two methods.One of the methods,is developed based on possibility theory.The performance of the reliability of the system is of p...In this article,mathematical modeling for the evaluation of reliability is studied using two methods.One of the methods,is developed based on possibility theory.The performance of the reliability of the system is of prime concern.In view of this,the outcomes for the failure are required to evaluate with utmost care.In possibility theory,the reliability information data determined from decision-making experts are subjective.The samemethod is also related to the survival possibilities as against the survival probabilities.The other method is the one that is developed using the concept of approximation of closed interval including the piecewise quadratic fuzzy numbers.In this method,a decision-making expert is not sure of his/her estimates of the reliability parameters.Numerical experiments are performed to illustrate the efficiency of the suggested methods in this research.In the end,the paper is concluded with some future research directions to be explored for the proposed approach.展开更多
The intrinsic optimum temperature for the development of ectotherms is one of the most important factors not only for their physiological processes but also for ecolog- ical and evolutional processes. The Sharpe-Schoo...The intrinsic optimum temperature for the development of ectotherms is one of the most important factors not only for their physiological processes but also for ecolog- ical and evolutional processes. The Sharpe-Schoolfield-Ikemoto （SSI） model succeeded in defining the temperature that can thermodynamically meet the condition that at a par- ticular temperature the probability of an active enzyme reaching its maximum activity is realized. Previously, an algorithm was developed by Ikemoto （Tropical malaria does not mean hot environments. Journal of Medical Entomology, 45, 963-969） to estimate model parameters, but that program was computationally very time consuming. Now, investi- gators can use the SSI model more easily because a full automatic computer program was designed by Shi et al. （A modified program for estimating the parameters of the SSI model. Environmental Entomology, 40, 462-469）. However, the statistical significance of the point estimate of the intrinsic optimum temperature for each ectotherm has not yet been determined. Here, we provided a new method for calculating the confidence interval of the estimated intrinsic optimum temperature by modifying the approximate bootstrap confidence intervals method. For this purpose, it was necessary to develop a new program for a faster estimation of the parameters in the SSI model, which we have also done.展开更多
The logarithmic moment estimations of parameters are proposed for two-parameter generalized Birnbaum-Saunders Logistic fatigue life distribution GBS-Logistic(α,β)under the full sample.The precisions of point estimat...The logarithmic moment estimations of parameters are proposed for two-parameter generalized Birnbaum-Saunders Logistic fatigue life distribution GBS-Logistic(α,β)under the full sample.The precisions of point estimations are investigated and compared with other point estimations by Monte-Carlo simulations.The approximate interval estimations of parameters are given by using Taylor expansion,and the precisions of approximate interval estimations are investigated by Monte-Carlo simulations.Finally,several examples show the feasibility of the methods.展开更多
Consider the model (1.6), where eij (j=1,…,Ni, i=1,2,…) are i.i.d.with mean 0 andwriance 1.Introduce a randomly weighted estimate βn defined by (1.8).Assuming e11 ～N(0, 1)and,the paper gives a necessary and suffic...Consider the model (1.6), where eij (j=1,…,Ni, i=1,2,…) are i.i.d.with mean 0 andwriance 1.Introduce a randomly weighted estimate βn defined by (1.8).Assuming e11 ～N(0, 1)and,the paper gives a necessary and sufficient condition for βn to be a consistent estimateof β0,and under some further restrictions a normal approximation fo βn is established whichcan be used in constructing a large sample confidence interval of β0. Finally, in the non-normalcase a theorem about the consistency of βn is proved.展开更多
文摘In this article,mathematical modeling for the evaluation of reliability is studied using two methods.One of the methods,is developed based on possibility theory.The performance of the reliability of the system is of prime concern.In view of this,the outcomes for the failure are required to evaluate with utmost care.In possibility theory,the reliability information data determined from decision-making experts are subjective.The samemethod is also related to the survival possibilities as against the survival probabilities.The other method is the one that is developed using the concept of approximation of closed interval including the piecewise quadratic fuzzy numbers.In this method,a decision-making expert is not sure of his/her estimates of the reliability parameters.Numerical experiments are performed to illustrate the efficiency of the suggested methods in this research.In the end,the paper is concluded with some future research directions to be explored for the proposed approach.
文摘The intrinsic optimum temperature for the development of ectotherms is one of the most important factors not only for their physiological processes but also for ecolog- ical and evolutional processes. The Sharpe-Schoolfield-Ikemoto （SSI） model succeeded in defining the temperature that can thermodynamically meet the condition that at a par- ticular temperature the probability of an active enzyme reaching its maximum activity is realized. Previously, an algorithm was developed by Ikemoto （Tropical malaria does not mean hot environments. Journal of Medical Entomology, 45, 963-969） to estimate model parameters, but that program was computationally very time consuming. Now, investi- gators can use the SSI model more easily because a full automatic computer program was designed by Shi et al. （A modified program for estimating the parameters of the SSI model. Environmental Entomology, 40, 462-469）. However, the statistical significance of the point estimate of the intrinsic optimum temperature for each ectotherm has not yet been determined. Here, we provided a new method for calculating the confidence interval of the estimated intrinsic optimum temperature by modifying the approximate bootstrap confidence intervals method. For this purpose, it was necessary to develop a new program for a faster estimation of the parameters in the SSI model, which we have also done.
基金supported by the National Natural Science Foundation of China under Grant No.11671264
文摘The logarithmic moment estimations of parameters are proposed for two-parameter generalized Birnbaum-Saunders Logistic fatigue life distribution GBS-Logistic(α,β)under the full sample.The precisions of point estimations are investigated and compared with other point estimations by Monte-Carlo simulations.The approximate interval estimations of parameters are given by using Taylor expansion,and the precisions of approximate interval estimations are investigated by Monte-Carlo simulations.Finally,several examples show the feasibility of the methods.
文摘Consider the model (1.6), where eij (j=1,…,Ni, i=1,2,…) are i.i.d.with mean 0 andwriance 1.Introduce a randomly weighted estimate βn defined by (1.8).Assuming e11 ～N(0, 1)and,the paper gives a necessary and sufficient condition for βn to be a consistent estimateof β0,and under some further restrictions a normal approximation fo βn is established whichcan be used in constructing a large sample confidence interval of β0. Finally, in the non-normalcase a theorem about the consistency of βn is proved.
