Reliability analysis of time-dependent cascade system with random cycle times

Reliability analysis of time-dependent 2-cascade and 3-cascade systems is carried out using stress/strength models. Each of the stress and strength variables is assumed to be deterministic or random fixed or random independent. The number of cycles in any period of time t is assumed to be random. The particular case when the number of cycles in any period of time t follows a Poisson distribution is also considered. The components are assumed to be identical and the attenuation factors k_i's are assumed to be constants. Also, expressions for the system reliability are obtained, and a few numerical results are computed when the stress and the strength distributions are exponential.