<正> Along the same line of research as in [1], in this paper, we consider the followingthree major problems. The first is to study, from the viewpoint of program-size complexity,the properties possessed by Mart...<正> Along the same line of research as in [1], in this paper, we consider the followingthree major problems. The first is to study, from the viewpoint of program-size complexity,the properties possessed by Martin-lof (M. L.) infinite random sequences. It is found thatM. L. infinite random sequences are normal and satisfy the law of iterated logarithm. Thesecond is to consider the effective generation of M. L. infinite random sequences. It isfound that by using a standard method (e. g., tossing a fair coin) we can choose M. L.infinite random sequences of any computable probability distribution. The last is how todefine the concept of infinite randomness for noncomputable probability distributions. Twotentative definitions are given, and one of them is discussed at length.展开更多
Suppose that (x_t,t≥0) is a stochastic process of the exponential type with P_θ(x_t∈B) =∫_B exp{θ_x - tψ(θ)}γ(t,x)V_t(dx),where θ∈Θ? (-∞,∞) and V_t is a measure. For testing the hypothesis θ≤θ_0 agains...Suppose that (x_t,t≥0) is a stochastic process of the exponential type with P_θ(x_t∈B) =∫_B exp{θ_x - tψ(θ)}γ(t,x)V_t(dx),where θ∈Θ? (-∞,∞) and V_t is a measure. For testing the hypothesis θ≤θ_0 againstθ>θ_0, we have found a class of truncated sequential tests with probability of the first kindof error not exceeding α, the expected observation time of tests being asymptoticallyminimal as α ↓0.展开更多
A Bayesian sequential testing method is proposed to evaluate system reliability index with reliability growth during development.The method develops a reliability growth model of repairable systems for failure censore...A Bayesian sequential testing method is proposed to evaluate system reliability index with reliability growth during development.The method develops a reliability growth model of repairable systems for failure censored test,and figures out the approach to determine the prior distribution of the system failure rate by applying the reliability growth model to incorporate the multistage test data collected from system development.Furthermore,the procedure for the Bayesian sequential testing is derived for the failure rate of the exponential life system,which enables the decision to terminate or continue development test.Finally,a numerical example is given to illustrate the efficiency of the proposed model and procedure.展开更多
文摘<正> Along the same line of research as in [1], in this paper, we consider the followingthree major problems. The first is to study, from the viewpoint of program-size complexity,the properties possessed by Martin-lof (M. L.) infinite random sequences. It is found thatM. L. infinite random sequences are normal and satisfy the law of iterated logarithm. Thesecond is to consider the effective generation of M. L. infinite random sequences. It isfound that by using a standard method (e. g., tossing a fair coin) we can choose M. L.infinite random sequences of any computable probability distribution. The last is how todefine the concept of infinite randomness for noncomputable probability distributions. Twotentative definitions are given, and one of them is discussed at length.
基金Project supported by the National Natural Science Foundation of China.
文摘Suppose that (x_t,t≥0) is a stochastic process of the exponential type with P_θ(x_t∈B) =∫_B exp{θ_x - tψ(θ)}γ(t,x)V_t(dx),where θ∈Θ? (-∞,∞) and V_t is a measure. For testing the hypothesis θ≤θ_0 againstθ>θ_0, we have found a class of truncated sequential tests with probability of the first kindof error not exceeding α, the expected observation time of tests being asymptoticallyminimal as α ↓0.
基金supported by the National Natural Science Foundation of China (70571083)the Research Fund for the Doctoral Program of Higher Education of China (20094307110013)
文摘A Bayesian sequential testing method is proposed to evaluate system reliability index with reliability growth during development.The method develops a reliability growth model of repairable systems for failure censored test,and figures out the approach to determine the prior distribution of the system failure rate by applying the reliability growth model to incorporate the multistage test data collected from system development.Furthermore,the procedure for the Bayesian sequential testing is derived for the failure rate of the exponential life system,which enables the decision to terminate or continue development test.Finally,a numerical example is given to illustrate the efficiency of the proposed model and procedure.
