On the Consecutive-k-of-n:F System

TLDR

The k‑of‑n:F system consists of n linearly or circularly ordered components that fail when k consecutive components fail, and the study examines its life‑distribution properties, including non‑i.i.d. scenarios. The study derives recursive formulas and bounds for system reliability in the i.i.d.

Abstract

The linear (circular) k-of-n:F system has n linearly (circularly) ordered components. Each component either functions or fails. The system fails i.f.f.k consecutive components fail. This paper provides, in the i.i.d. case, recursive formulas and bounds for computing system reliability. It considers properties of system life distributions and, in the non i.i.d. case, questions of optimal system design.