Studies in Cascade ReliabilityߞII

Part 1 considers the cascade system with random attenuation factor; the 2-cascade system is studied under the assumption that stress and strength are exponential, gamma, or s-normal variates, and the 3-cascade system under the assumption that they are both exponential. Moments of the system reliability, as a function of the random attenuation vector, are numerically obtained and tabulated, assuming the attenuation factors to be beta distributed. Gamma type functions are fitted to the reliabilities by least squares; the fits are good. Part 2 considers the cascade system subjected to stresses arriving in a Poisson process; expressions for the reliability of the system are obtained for the 2- and 3-cascade systems. Characteristics of the time-to-failure distribution are derived. The coefficients of variation are independent of the parameter of the Poisson process. The time for which the system will work with a given reliability is obtained numerically when the stress and strength distributions are both exponential, gamma, or s-normal.