# System Reliability

This page is designed to give the reliability of consecutive-type systems with n independent components.

## What are Consecutive-Type Systems?

Consecutive-type systems are systems that fail when some pattern of failed components occurs.

The basic assumptions are:

• Each component is either failed or operational (on/off).
• Components are independent.
• All components have the same probability of failure (within a specific time interval).

There are three well known consecutive-type systems:

• Consecutive-k-out-of-n: F Systems These systems consist of n components, and fail if there is a sequence of k consecutive failed components.
• m-consecutive-k-out-of-n: F Systems These systems consist of n components, and fail if there are m sequences of k consecutive failed components.
• r-within-k-out-of-n: F Systems These systems consist of n components, and fail if there are r failed components within a "window" of k consecutive components ( r < k ).

A series system with n components, which fails if there is at least one failed component, is a special case of the Consecutive-k-out-of-n:F system with k = 1.

A parallel system with n components, which fails only if all the components fail, is a special case of the Consecutive-k-out-of-n:F system with k = n.

To Compute the reliability of a consecutive-type system, select a system: