Faulty Server Detection - Identify Outlier Servers by Error Rate

Question

## Problem

You have a list of server metrics over a time window: `[(server_id, requests, errors)]`. A server is "faulty" if its error rate exceeds the fleet-wide mean error rate by more than `k` standard deviations.

Return the IDs of all faulty servers, sorted lexicographically.

```python
def faulty_servers(
    metrics: list[tuple[str, int, int]],
    k: float
) -> list[str]:
```

Error rate for a server = `errors / requests`. Exclude servers with 0 requests.

## Example

```
metrics = [("s1",1000,10),("s2",1000,200),("s3",1000,8),("s4",1000,12)]
# rates: 0.01, 0.20, 0.008, 0.012; mean~0.0575, std~0.094
# k=1.0: s2 is > mean+1*std
Output: ["s2"]
```

## Follow-ups

1. Why is this approach sensitive to outliers in the standard deviation calculation itself? What robust alternative would you use?
2. How would you adapt this to detect faulty servers in a rolling 5-minute window from a real-time stream?
3. What if error rate alone is insufficient -- how would you combine multiple signals (latency, restarts)?
4. Write a SQL query to identify faulty servers from a table `server_metrics(server_id, requests, errors)`.

Faulty Server Detection - Identify Outlier Servers by Error Rate

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