Redundancy Calculator

N+1 redundancy means the system has N components required for full operation plus 1 additional spare component. If any single component fails, the spare takes over without service interruption. Examples: N+1 power supplies in a server, N+1 cooling units in a data center, N+1 network uplinks. N+1 tolerates 1 failure; N+2 tolerates 2 simultaneous failures.

2N redundancy duplicates every component: the system has N active components and N standby (or active) spares. This provides full redundancy with no single point of failure. Examples: dual power feeds from separate UPS systems, dual network paths from separate providers. 2N redundancy typically doubles capital cost but provides the highest resilience.

A k-of-n system requires at least k of n total components to be operational. For example, a RAID 5 array with 4 drives requires 3 of 4 drives working (3-of-4). If any 1 drive fails, the array continues operating; if 2 fail simultaneously, it fails. K-of-n redundancy generalizes N+1 (which is N-of-(N+1)) and majority voting systems used in fault-tolerant computing.

For n identical parallel components where k must work: availability = 1 - P(fewer than k working). The probability of exactly j components working = C(n,j) * A^j * (1-A)^(n-j), where A is individual component availability. Sum P(j) for j = 0 to k-1 and subtract from 1. For simple N+1 with 2 components: A_sys = 1 - (1-A)^2 = 2A - A^2.

Active (hot standby) redundancy: all redundant components are running in parallel and immediately take load if one fails. Recovery time is near-zero. Standby (cold or warm standby) redundancy: spare components are off or in reduced-power mode and must be started/activated on failure. Recovery time ranges from seconds (warm standby) to minutes (cold standby). Active redundancy offers better MTTR at higher power cost.