Inference on Reliability for Cascade Model (Journal of Informatics and Mathematical Sciences, 2012)
In this paper we consider two cases to obtain the system reliability for cascade model. For the first case we consider one-parameter exponential strength and two-parameter gamma stress. Under this assumption the reliability of the system in general terms is obtained. Secondly we consider two-parameter exponential strength and one-parameter gamma stress to obtain an expression for the reliability of a 3-cascade system. For both the cases all stress-strengths are random variables with given density. In all these cases numerical integration is used to evaluate the reliability for cascade system. Some numerical values of $R( 1 )$, $R( 2 )$, $R( 3 )$ and $R_{3} $ for particular values of the parameters involved are tabulated at the end.
Keywords: Stress-strength model; Cascade model; One and two-parameter exponential and gamma distributions; Standby redundancy; Reliability