Redundancy is the creation of functionally identical or comparable resources of a technical system for a trouble free fail safe operation. Redundancy is not actually specific for Computing, but particularly in case of Cloud Computing, this is very important point to mention, which helps in increasing reliability of the overall system.
Redundancy is the name of Fail Safe behavior
There are different types of redundancy. The functional redundancy aims to design safety systems in parallel, thus ensuring the less probability of failure of a component of a service. The software of a redundant system should be different as possible in the following aspects: specification (different teams), specification language, programming, programming language compilers.
Hot redundancy means that the system perform the function of multiple systems in parallel. Cold redundancy means that in the system, several functions are available in parallel, but only one is working. Standby redundancy or passive redundancy adds additional resources which will be turned on only in case of failure or malfunction in the execution of the tasks of the already operating unit. N +1 redundancy means that a system of n number of functional units which are active at a time and consists of a passive standby unit.
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In a homogeneous redundancy same components are working in parallel whereas in the diverse redundancy to systems work together by using different components from different manufacturers.
Fail Safe Behavior of Redundant Systems

Fail safe means that in case of failure the failed system is no longer available and occupies a manageable starting state. The failure of a component must lead by additional measures in the schedule to a manageable outcome. An example would be compared with the automatic provision of another server in case of failure of one server.
Fail Passive means that the system of two fail-safe systems must be designed and equipped with error detection and error suppression. Fail Operational means that the facility continues to operate under fault conditions.
Conclusion on Redundancy
Redundancy as we said, not specific for computing. Calculating the probability of system failure, the system of Redundancy is adopted :

Where n is the number of components, p is the probability of all components failing where Redundancy will be deployed.
