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For a device that listens for a spoken trigger phrase, both kinds of mistakes matter: missing the phrase and reacting when it was not spoken. A practical goal is to reduce the false negative rate, while also requiring that the false positive rate stay below one false alarm per 24 hours of use.

Using Two Error Rates in a Voice-Trigger Goal

Which metric setup best fits a voice-activation detector goal?

A device that turns on when no trigger phrase was spoken has produced a false positive.

In a voice-trigger system, the objective is to reduce the _____ rate while keeping false alarms low.

Match each trigger-detection metric term to its meaning in a smart speaker system.

Order the steps for comparing wake word systems under a dual-objective goal.

Question:
In a brief analytical response, explain how a target-setting framework can treat missed detections and false alarms differently for a voice-activated assistant.

Sample answer:
The two error rates both matter, but they play different roles in the goal. The false alarm rate is the satisficing condition: the detector is only acceptable if it triggers no more than two false activations per day. Once a detector meets that limit, the missed-detection rate becomes the optimizing target, so the best model is the one that catches the most real wake words.

Key points:
- False alarms are activations when the wake word was not spoken.
- Missed detections are failures to activate when the wake word was spoken.
- Missed-detection rate is the quantity to minimize.
- False alarms must stay at or below two per day.
- The best detector is chosen from models that satisfy the false-alarm limit.

Rubric:
A strong response correctly defines both error types, identifies missed-detection rate as the optimizing metric, states the false-alarm constraint, and explains that only models meeting the constraint are compared on the optimizing metric.

Why do the two wake-word error rates serve different purposes in the target goal?

Case context:
A safety team is evaluating several sensors that detect smoke in a storage warehouse. Any sensor that raises more than 2 false alarms per day is too disruptive to use. The remaining sensors differ in how often they fail to detect a real fire.

Question:
How should the team filter the sensors, and which metric should decide the final selection?

Sample answer:
First remove every sensor that exceeds the 2-false-alarm-per-day limit, because those options do not satisfy the required operating constraint. Then compare the false negative rates of the sensors that remain and choose the one with the smallest false negative rate, since that is the metric to optimize among acceptable options.

Key points:
- Use the false-alarm limit as a requirement for eligibility.
- Discard any sensor that is too noisy.
- Among the sensors that qualify, compare false negative rates.
- Pick the qualifying sensor with the lowest false negative rate.

Rubric:
The response should treat the false-alarm limit as a gatekeeper constraint and then select the eligible sensor with the lowest false negative rate.

Choose a warehouse sensor under a hard false-alarm limit.

Question:
Answer in one to three sentences. Explain what a false positive and a false negative mean for a system that decides whether to trigger an alert.

Sample answer:
A false positive is an alert that sounds when no real event happened. A false negative is a real event that occurs, but the system fails to trigger the alert.

Key points:
- False positive: alert triggered without the event.
- False negative: event occurs but no alert is triggered.

Rubric:
The answer must correctly define a false positive as an unnecessary alert and a false negative as a missed alert when the event really occurred.

What do false positives and false negatives mean in an alert system?

Which detector satisfies the false-alarm constraint and can be optimized?

A detector can have the lowest missed-detection rate among the candidates and still fail the overall goal if it produces too many false alarms.

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