Abstract: An m-consecutive-k-out-of-n; F reliability system consists of n linearly arranged, independently functioning (or Markov-dependent) components, and fails iff k consecutive component failures occur (disjointly) m or more times. We employ the Stein-Chen method to obtain Poisson approximations for the reliability of such systems. The i.i.d., independent but non-ident ical, and stationary (rth order,r<=k) Markov dependent cases are considered.
Key words and phrases: Consecutive k-out-of-n: F systems, Stein-Chen method, failure runs, rth order Markov dependence.