N+1 is not a universal label
A four-unit design requiring three is tolerant of one missing unit. Its service probability depends on unit p and independence, not the N+1 phrase alone.
Probability
System Availability Outcome Table Calculator
Enumerate every available-unit state in an independent redundant system, classify quorum service, and reconcile system availability with expected state cost.
REDUNDANT-SYSTEM STATE SPACE
See every quorum state instead of hiding redundancy inside one percentage
For identical independent units, the model assigns exact binomial probability to each possible count available, labels service status, and multiplies each state by its entered consequence.
System service availability -
System outage probability -
Expected state cost -
Expected available units -
Expected unavailable units -
Service quorum -
LIVE DECISION RECORD
Redundant-unit outcome and cost table
All k=0 through n states are mutually exclusive and exhaustive; cost contribution is probability times state cost.
| Available units | Missing units | State probability | Service state | State cost | Expected-cost contribution |
|---|
CURRENT CALCULATION PROCESS
Formula, current substitution, intermediate values, and reconciliation
P(K=k)=C(n,k)p^k(1-p)^(n-k); A_sys=sum from k=r to nP(K=k); E[C]=sum over k of P(K=k)C_k
| Symbol | Meaning and unit | Current value |
|---|---|---|
| units | Total redundant units - Identical units represented in the state table. | 4 |
| unitAvailabilityPct | Availability per unit (%) - Stable independent probability that one unit is available. | 97.5 |
| requiredUnits | Units required for service - Quorum count; cannot exceed total units. | 3 |
| costPerMissingUnit | Cost per missing unit - Degraded-service consequence for each unavailable unit. | 4000 |
| outageCost | Additional system-outage cost - Extra consequence added when available units fall below quorum. | 75000 |
Waiting for valid inputs.
WHO THIS MODEL SERVES
A scoped decision aid, not a universal forecast
Primary audience: Architecture, SRE, reliability, capacity, and finance teams comparing identical-unit redundancy and quorum choices.
Decision boundary: Use for exchangeable independent units and a count-based quorum; topology, repair dynamics, and common-cause dependencies require a richer state model.
HOW TO BUILD THE STATE TABLE
Five steps from architecture to expected consequence
- Count the interchangeable units whose simultaneous state matters.
- Enter per-unit availability from a consistent observation regime.
- Set the minimum unit count that genuinely sustains the defined service.
- Separate per-missing-unit degradation cost from the additional outage consequence.
- Review every state, confirm 100% probability closure, and export the current architecture record.
REDUNDANCY FUNDAMENTALS
Five state-space distinctions
- Exchangeable units
- Every unit is assigned the same availability probability.
- Independence
- One unit's state does not change another unit's probability in this model.
- Quorum
- The minimum available-unit count required for service classification.
- Degraded service
- Quorum is met but one or more units are unavailable.
- Exhaustive outcomes
- Exactly one count k from zero through n occurs, so row probabilities must sum to one.
FORMULA AND DEFAULT SUBSTITUTION
Aggregate only after every state is priced
P(K=k)=C(n,k)p^k(1-p)^(n-k); service when k>=r
Defaults use n=4, p=0.975, and r=3. The table computes five exact rows. For each row, missing-unit cost is (4-k) x 4,000; when k<3, 75,000 is added before multiplying by the row probability.
DEEPER OUTCOME ANALYSIS
Three architecture questions revealed by the table
Degradation can dominate expected cost
Rare outage rows may have severe costs, but frequent one-unit-missing rows can contribute more expected cost when degradation is expensive.
Common cause erodes redundancy
Power, software, network, or maintenance dependencies can make multiple units fail together, invalidating the binomial gain.
WORKED ARCHITECTURE CASES
Two quorum choices with distinct service promises
Four chillers, three required
The default table distinguishes full capacity at k=4, degraded but available service at k=3, and outage at k<=2. The expected-cost column can justify whether another spare or better unit reliability deserves review.
Quorum exceeds fleet boundary
Entering five required units for a four-unit fleet is rejected rather than returning zero availability, because the architecture definition itself is invalid and should not enter an audit record.
STATE-SPACE TERMINOLOGY
Six terms used in the ledger
- Per-unit availability
- Probability that one exchangeable unit is available.
- State
- One possible count of currently available units.
- Quorum
- Minimum count classified as service-capable.
- Full service
- All modeled units are available.
- Outage state
- Available count is below the required quorum.
- Expected state cost
- Sum of each state cost weighted by its exact probability.
EVIDENCE RETENTION
Record the dependency claim behind p
Retain component scope, availability measurement interval, quorum test evidence, topology diagram, shared-resource inventory, degraded-service cost basis, and outage consequence approval. Record exclusions and common-cause review explicitly.
LIMITS AND EXCLUSIONS
Boundaries of the binomial architecture model
- Units are identical in probability and statistically independent.
- Only simultaneous availability states are modeled; transitions and repair queues are absent.
- Quorum depends only on count, not location, role, capacity, or network topology.
- State costs are linear per missing unit plus one outage increment.
- This table is not a fault-tree, Markov, safety, or certification analysis.
RELIABLE SOURCES
Primary references for state probabilities and availability
REDUNDANCY OUTCOME FAQ
Questions about quorum and state cost
Is this the same as single-system MTBF/MTTR availability?
No. It starts with a per-unit availability probability and builds the distribution of simultaneous unit states under independence.
Why list all states?
The full table prevents hidden aggregation: degraded service, full service, and outage states each retain their probability and consequence.
What does quorum mean here?
Service is classified available when at least the entered number of units is available, regardless of which named units they are.
Can units have different availability?
Not in this binomial version. Unequal units need a Poisson-binomial or explicit state-space model.
Does expected state cost predict one invoice?
No. It is the probability-weighted average across mutually exclusive states for the chosen exposure basis.
How should common-cause failures be handled?
Do not force them into independent p values. Add shared-cause states or use a fault-tree/Markov model reviewed by a reliability specialist.
IMPORTANT ARCHITECTURE NOTE
Independence must be demonstrated in the topology
A high calculated system availability can be false precision when units share failure modes. Use this table to expose assumptions, then test them against the real architecture.