### Cascade System with $Pr(X<Y<Z)$

#### Abstract

The paper considers a $n$-cascade system with $P(X<Y<Z)$ where $Y$ is the stress on the component subjected to two strengths $X$ and $Z$.\ Reliability expressions of an $n$-cascade system is obtained when stress-strength both are either Exponential or Rayleigh or Lindley. It is also considered the cases when both strengths are one parameter exponential and stress follows Lindley distributions and when both strengths are one parameter exponential and stress follows two parameters gamma distributions. The numerical values $R(1)$, $R(2)$, $R(3)$ and $R_3$ have also been computed and provided in tabular forms for some specific values of the parameters.

#### Keywords

Cascade system; Stress-Strength reliability; Exponential; Rayleigh; Gamma distribution

#### Full Text:

PDFDOI: http://dx.doi.org/10.26713%2Fjims.v5i1.105

eISSN 0975-5748; pISSN 0974-875X