Statistica Sinica

Anant P. Godbole

Abstract:Anm-consecutive-k-out-of-n;Freliability system consists ofnlinearly arranged, independently functioning (or Markov-dependent) components, and fails iffkconsecutive component failures occur (disjointly)mor 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:Consecutivek-out-of-n:Fsystems, Stein-Chen method, failure runs,rth order Markov dependence.