Studies in Cascade Reliability-I

Abstract

An n-Cascade system is defined as a special type of In section 2, we formulate a general problem of Reliability standby system with n components. A component fails if the stress of an n-Cascade system. Section 3 deals with exponential on it is not less than its strength. When a component in cascade fails, stress and strength distributions. Explicit expressions for the next in standby is activated and will take on the stress. However, n-Cascade system reliability are obtained, a general recursive the stress on this component will be a multiple k times the stress that ' acted on its predecessor. The system fails if due to an initial stress, rule is indicated for obtaining these expressions and for k = each of the components in succession fails. 1, a finite series expansion is obtained. Sections 4 and 5 deal The stress is random and the component strengths are independent with the 2-cascade system where X and Y both follow the and identically distributed variates, with specified probability func- Gamma and the Normal distributions respectively. tions; k is constant. Expressions for system reliability are obtained when the stress and strength distributions are exponential. Reliability values for a 2-cas- 2. THE n-CASCADE MODEL cade system with Gamma and Normal stress and strength distributions are computed, some of which are presented graphically