In the present work, it is assumed that the n-components are arranged in the hierarchial order. The n-cascade system surviving with loss of m components by k number of attacks is studied; the general equation for the reliability is obtained for the above said system; and the system reliability is computed numerically for 6-cascade system for 2-number of attacks.
I. IntrodutionTime dependent stress strength models by considering with the repeated application of stress and also considering the change of the distribution of strength with time. "Stress" is used to indicate any agency that tends to induce "failure", while "Strength" indicates any agency resisting "failure". "Failure is defined to have occurred when the actual stress exceed the actual strength.There is uncertainty about the stress and strength random variables at any instant of time and also about the behavior of the random variables with respect to time and cycles .The two terms "deterministic" and "random fixed" are used to describe these two uncertainties .In deterministic , the variables assumes values that are exactly known a priori .Random fixed refers to the behavior of the variable with respect to time is fixed or the variable varies in time in a known manner .The failure of components under repeated stresses had been investigated primarily .Repeated stresses are characterized by the time, each load applied and the behavior of time intervals between the application of loads.We prefer n R the reliability after n cycles , to R(t), the reliability at time t , where t is continuous .Simply when cycle times are deterministically known R(t)= n R , n t < t ≤ 1 In the present paper, we have discussed deterministic stress and random fixed strength and vice versa, we had take Exponential and Rayleigh distributions. Reliability computations were done for different cycle lengths .The result is that the system reliability rapidly changes in Rayleigh distribution than the Exponential distribution.
In this paper general expression of reliability has been derived for time dependent stress strength model if stress is random independent and strength is random fixed for the following cases. (i).Stress follow Pareto distribution and strength follow finite mixture of exponential distribution. (ii).Stress follow exponential distribution and strength follow finite mixture of Pareto distribution.
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