A class of lifetime distributions, new better than equilibrium in expectation （NBEE）, and its dual, new worse than equilibrium in expectation （NWEE）, are studied based on the comparison of the expectations of life...A class of lifetime distributions, new better than equilibrium in expectation （NBEE）, and its dual, new worse than equilibrium in expectation （NWEE）, are studied based on the comparison of the expectations of lifetime X and its equilibrium Xo. The relationships of the NBEE （NWEE） and other lifetime distribution classes are discussed. It is proved that the NBEE is very large, and increasing failure rate （IFR）, new better than used （NBU） and the L class are its subclasses. The closure properties under two kinds of reliability operations, namely, convolution and mixture, are investigated. Furthermore, a Poisson shock model and a special cumulative model are also studied, in which the necessary and sufficient conditions for the NBEE （NWEE） lifetime distribution of the systems are established. In the homogenous Poisson shock model, the system lifetime belongs to NBEE（NWEE） if and only if the corresponding discrete failure distribution belongs to the discrete NBEE（NWEE）. While in the cumulative model, the system has an NBEE lifetime if and only if the stochastic threshold of accumulated damage is NBEE.展开更多
We consider how to identify the transition rates of ion channels with the underlying scheme which is kinetically modelled as time-homogeneous Markov chain. A Markov chain inversion approach is developed to perform a d...We consider how to identify the transition rates of ion channels with the underlying scheme which is kinetically modelled as time-homogeneous Markov chain. A Markov chain inversion approach is developed to perform a difficult inversion to identify the transition rates from the parameters characterizing the lifetime distributions at a small number of states, although it is straightforward to derive the lifetime distribution. The general explicit equations relating the parameters of the lifetime distribution to the tran- sition rates are derived and transition rates are then obtained as roots to this system of equations. The concrete solutions are proposed to the basic and regular schemes such as linear, star-graph branch and loop. Useful conclusions and solutions to realistic schemes are also included to show its efficiency.展开更多
基金The National Natural Science Foundation of China(No. 10801032)
文摘A class of lifetime distributions, new better than equilibrium in expectation （NBEE）, and its dual, new worse than equilibrium in expectation （NWEE）, are studied based on the comparison of the expectations of lifetime X and its equilibrium Xo. The relationships of the NBEE （NWEE） and other lifetime distribution classes are discussed. It is proved that the NBEE is very large, and increasing failure rate （IFR）, new better than used （NBU） and the L class are its subclasses. The closure properties under two kinds of reliability operations, namely, convolution and mixture, are investigated. Furthermore, a Poisson shock model and a special cumulative model are also studied, in which the necessary and sufficient conditions for the NBEE （NWEE） lifetime distribution of the systems are established. In the homogenous Poisson shock model, the system lifetime belongs to NBEE（NWEE） if and only if the corresponding discrete failure distribution belongs to the discrete NBEE（NWEE）. While in the cumulative model, the system has an NBEE lifetime if and only if the stochastic threshold of accumulated damage is NBEE.
基金Supported by National Natural Science Foundation of China (1087105411171101)+1 种基金Provincial Natural Science Foundation of Hunan (09JJ6016)Scientific Research Fund of Hunan Provincial Education Department (10B073)
文摘We consider how to identify the transition rates of ion channels with the underlying scheme which is kinetically modelled as time-homogeneous Markov chain. A Markov chain inversion approach is developed to perform a difficult inversion to identify the transition rates from the parameters characterizing the lifetime distributions at a small number of states, although it is straightforward to derive the lifetime distribution. The general explicit equations relating the parameters of the lifetime distribution to the tran- sition rates are derived and transition rates are then obtained as roots to this system of equations. The concrete solutions are proposed to the basic and regular schemes such as linear, star-graph branch and loop. Useful conclusions and solutions to realistic schemes are also included to show its efficiency.
