This paper investigates the comparison problem of the reliability index between a parallel and a cold-standby system,both of which are consisting of two identical units.On the contrary to the general intuitive result,...This paper investigates the comparison problem of the reliability index between a parallel and a cold-standby system,both of which are consisting of two identical units.On the contrary to the general intuitive result,we proved that,under the condition that the system is shocked by a Poisson stream,the life time of the parallel system is longer than that of the cold-standby one in the sense of probability.展开更多
Based on the stochastic uncertainty of the system’s operating environment,this research presents statistical inferences on the mean time to failure(MTTF)of a K-out-of-N:G nonrepairable system model with switching fai...Based on the stochastic uncertainty of the system’s operating environment,this research presents statistical inferences on the mean time to failure(MTTF)of a K-out-of-N:G nonrepairable system model with switching failure under Poisson shocks.The standby component is switched to the operating component when an operating component fails,with a switching failure probability of p.The MTTF of the system is derived by using the Markov process theory and the Laplace transform for two cases where the shock threshold is a constant value or a random variable.The maximum likelihood estimator(MLE)of the MTTF is obtained,and based on this estimator,asymptotic confidence interval estimation and hypothesis testing are performed.Based on the setting of the basic parameter values,the MTTF under two different cases of the shock threshold is compared.The effect of each parameter on the MTTF is analyzed in numerical simulation.The effectiveness of the above statistical inference methods is also verified by numerical simulation.展开更多
In this paper,a two-dissimilar-component cold standby repairable system maintained by a repairmanis investigated.The system fails due to either intrinsic factors or external shocks.Assume that shocks arrive according ...In this paper,a two-dissimilar-component cold standby repairable system maintained by a repairmanis investigated.The system fails due to either intrinsic factors or external shocks.Assume that shocks arrive according to a stepwise Poisson process,the intensity of which varies with respect to the number of failures of the working component.Repair after failure is imperfect.Using the supplementary variable method and the vector Markov process theory,we obtain some important reliability index for the system.By the renewal reward theorem,an optimal replacement policy N∗is derived by minimising the average cost rate of the system.Numerical examples are presented to validate the theoretical results.展开更多
The study aims at modelling and assessment of survival probability of a component experiencing two kinds of shocks namely, damage shock and fatal shock. Shocks are occurring randomly in time as events of a Poisson Pro...The study aims at modelling and assessment of survival probability of a component experiencing two kinds of shocks namely, damage shock and fatal shock. Shocks are occurring randomly in time as events of a Poisson Process. The two cases of fixed/random threshold of components are studied. Survival probabilities of proposed models are derived. Maximum likelihood estimators (MLEs) of survival probabilities are obtained using the data from life testing experiments. Fisher information and asymptotic distribution of MLEs of parameters are obtained when a constant threshold is considered. Computation and comparison of estimators of two cases (constant threshold and random threshold) are made through simulation studies. The study recommends the consideration of threshold as a random variable.展开更多
文摘This paper investigates the comparison problem of the reliability index between a parallel and a cold-standby system,both of which are consisting of two identical units.On the contrary to the general intuitive result,we proved that,under the condition that the system is shocked by a Poisson stream,the life time of the parallel system is longer than that of the cold-standby one in the sense of probability.
基金supported by the National Natural Science Foundation of China[grant number 72071175]the Project of Hebei Key Laboratory of Software Engineering[grant number 22567637H]the Basic Innovative Research and Cultivation Project of Yanshan University[grant number 2023LGZD003].
文摘Based on the stochastic uncertainty of the system’s operating environment,this research presents statistical inferences on the mean time to failure(MTTF)of a K-out-of-N:G nonrepairable system model with switching failure under Poisson shocks.The standby component is switched to the operating component when an operating component fails,with a switching failure probability of p.The MTTF of the system is derived by using the Markov process theory and the Laplace transform for two cases where the shock threshold is a constant value or a random variable.The maximum likelihood estimator(MLE)of the MTTF is obtained,and based on this estimator,asymptotic confidence interval estimation and hypothesis testing are performed.Based on the setting of the basic parameter values,the MTTF under two different cases of the shock threshold is compared.The effect of each parameter on the MTTF is analyzed in numerical simulation.The effectiveness of the above statistical inference methods is also verified by numerical simulation.
文摘In this paper,a two-dissimilar-component cold standby repairable system maintained by a repairmanis investigated.The system fails due to either intrinsic factors or external shocks.Assume that shocks arrive according to a stepwise Poisson process,the intensity of which varies with respect to the number of failures of the working component.Repair after failure is imperfect.Using the supplementary variable method and the vector Markov process theory,we obtain some important reliability index for the system.By the renewal reward theorem,an optimal replacement policy N∗is derived by minimising the average cost rate of the system.Numerical examples are presented to validate the theoretical results.
文摘The study aims at modelling and assessment of survival probability of a component experiencing two kinds of shocks namely, damage shock and fatal shock. Shocks are occurring randomly in time as events of a Poisson Process. The two cases of fixed/random threshold of components are studied. Survival probabilities of proposed models are derived. Maximum likelihood estimators (MLEs) of survival probabilities are obtained using the data from life testing experiments. Fisher information and asymptotic distribution of MLEs of parameters are obtained when a constant threshold is considered. Computation and comparison of estimators of two cases (constant threshold and random threshold) are made through simulation studies. The study recommends the consideration of threshold as a random variable.
