论文信息 - FAILURE TIME DISTRIBUTION UNDER A δ-SHOCK MODEL AND ITS APPLICATION TO ECONOMIC DESIGN OF SYSTEMS

FAILURE TIME DISTRIBUTION UNDER A δ-SHOCK MODEL AND ITS APPLICATION TO ECONOMIC DESIGN OF SYSTEMS

Suppose that shocks arrive and act on a system according to a Poisson distribution with mean rate of arrival equal to λ shock(s) per unit time. A δ-shock failure model is proposed in this paper, which assumes that when a system is acted on by a shock, it will recover fully in time δ(>0), and after that it will function as if no shock had occurred before. If the time lag between two successive shocks is less than δ, the second shock will cause failure of the system. Theoretical expressions related to the distribution of the failure time of the system are derived. These results can be used to optimize the design of a system from a costing point of view.

[1] I. Olkin,et al. A generalized bivariate exponential distribution , 1967 .

[2] Albert W. Marshall,et al. Shock processes by aftereffects and multivariate lack of memory , 1984 .

[3] Henry W. Block,et al. A Continuous, Bivariate Exponential Extension , 1974 .

[4] Keunkwan Ryu,et al. An Extension of Marshall and Olkin's Bivariate Exponential Distribution , 1993 .

[5] Stephen Wolfram,et al. Mathematica: a system for doing mathematics by computer (2nd ed.) , 1991 .

[6] I. Olkin,et al. A Multivariate Exponential Distribution , 1967 .

[7] Henry W. Block,et al. A Characterization of a Bivariate Exponential Distribution , 1977 .

[8] D. P. Gaver,et al. Random Hazard in Reliability Problems , 1963 .

[9] Ushio Sumita,et al. Distribution properties of the system failure time in a general shock model , 1984, Advances in Applied Probability.

[10] A. W. Marshall,et al. Shock Models and Wear Processes , 1973 .

[11] F. Downton. Bivariate Exponential Distributions in Reliability Theory , 1970 .

[12] J. G. Shanthikumar,et al. General shock models associated with correlated renewal sequences , 1983 .

[13] S. Ross. Generalized Poisson Shock Models. , 1981 .