# Availability Maths — System Design Interview Prep

Source: https://www.skillbyai.com/en/system-design-interview/e-avail

> Nines, chains and redundancy.

## Series multiply, redundancy compounds

Availability is often quoted in **nines**: 99.9% allows about 8.8 hours of downtime per year, 99.99% about 53 minutes. Components in **series** multiply, so a chain is less available than its weakest link. **Redundant** independent replicas raise availability because all must fail at once. Real failures are often correlated (same region, same bad deploy), so the formulas give an upper bound.

## Downtime budgets and redundancy, run

I ran this with Python 3.12.3 using only the standard library; inputs are fixed or seeded, so the output is reproducible. Three components in series give 99.79%; duplicating the app and database tiers raises the total to about 99.99%, now limited by the single load balancer.

```python
# Availability: nines, serial chains and redundancy
MIN_PER_YEAR = 365 * 24 * 60
for a in (0.99, 0.999, 0.9999, 0.99999):
    print(f"{a:.3%} -> {MIN_PER_YEAR * (1 - a):8.1f} min/year downtime")

lb, app, db = 0.9999, 0.999, 0.999
serial = lb * app * db
print(f"LB -> app -> DB in series: {serial:.4%}")

def parallel(a, n):              # n independent replicas, any one is enough
    return 1 - (1 - a) ** n

print(f"two app replicas         : {parallel(app, 2):.6%}")
print(f"with 2 apps + 2 DBs      : {lb * parallel(app, 2) * parallel(db, 2):.4%}")
```

Output:

```
99.000% ->   5256.0 min/year downtime
99.900% ->    525.6 min/year downtime
99.990% ->     52.6 min/year downtime
99.999% ->      5.3 min/year downtime
LB -> app -> DB in series: 99.7901%
two app replicas         : 99.999900%
with 2 apps + 2 DBs      : 99.9898%
```

## Find the single points of failure

After drawing the design, point at each box and ask "what happens if this dies?"

**Quiz:** What happens to availability when components are chained in series?

- [ ] It becomes 100%
- [ ] It increases
- [ ] It stays equal to the best component
- [x] It decreases, because availabilities multiply

*Answer:* It decreases, because availabilities multiply. Each extra dependency is another way to fail.