Redundancy (engineering)

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In engineering, redundancy is the duplication of critical components of a system with the intention of increasing reliability of the system, usually in the case of a backup or fail-safe.

In many safety-critical systems, such as fly-by-wire and hydraulic systems in aircraft, some parts of the control system may be triplicated.^[1] An error in one component may then be out-voted by the other two. In a triply redundant system, the system has three sub components, all three of which must fail before the system fails. Since each one rarely fails, and the sub components are expected to fail independently, the probability of all three failing is calculated to be extremely small. Redundancy may also be known by the terms "majority voting systems"^[2] or "voting logic".^[3]

Contents 1 Forms of redundancy 2 Calculating the Probability of System Failure 3 See also 4 References 5 External links

[edit] Forms of redundancy

There are four major forms of redundancy, these are:

• Hardware redundancy, such as DMR and TMR
• Information redundancy, such as Error detection and correction methods
• Time redundancy, including transient fault detection methods such as Alternate Logic
• Software redundancy such as N-version programming

[edit] Calculating the Probability of System Failure

Each duplicate component added to the system decreases the probability of system failure according to the formula:

P =

where:

• n - number of components
• c p_i - probability of component i failing
• P - the probability of all components failing (system failure)

This formula assumes independence of failure events. That means that the probability of a component B failing given that a component A has already failed is the same as that of B failing when A has not failed. There are situations where this is unreasonable, such as using two power supplies connected to the same socket, whereby if one socket failed, the other would too.

It also assumes that at only one component is needed to keep the system running. If m components are needed for the system to survive, out of n, the probability is failure is

1 − ((1 − p)^{(m − n)} * _nC^m) , Assuming all components have equal probability, p, of failure

This model is probably unrealistic in that it assumes that components are not replaced in time when they fail.

[edit] See also

Common mode failure Data redundancy Double switching Fault tolerant design Radiation hardening Factor of safety

Reliability engineering Reliability theory of aging and longevity Safety engineering Self-healing ring MTBF

[edit] References

1. ^  Redundancy Management Technique for Space Shuttle Computers (PDF), IBM Research
2. ^ Majority voting systems
3. ^ Designing Integrated Circuits to Withstand Space Radiation
4. ^ Using powerline as a redundant communication channel

[edit] External links

• Secure Propulsion using Advanced Redundant Control