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: