Conditional Residual Lifetimes of $(n-k+1)$-out-of-$n$ Systems with Mixed Erlang Components (Journal of Mathematical Study, 2017)
We consider an $(n-k+1)$-out-of-$n$ system with component lifetimes beingcorrelated. The main objective of this paper is to study the conditional residual lifetimeof an $(n-k+1)$-out-of-$n$ system, given that at a fixed time a certain number ofcomponents have failed, assuming that the component lifetimes follow a multivariateErlang mixture. Comparison studies of the stochastic ordering of the $(n-k+1)$-out-of-$n$ system are presented. Several examples are presented to illustrate and confirm ourresults.
Keywords: Conditional mean residual lifetime; multivariate Erlang mixture; $(n-k+1)$-out-of-$n$ system; dependence structure; exchangeable variables.