# How to measure how well our service detects malfunctioning parts with different percentages?

I am running an algorithm to detect malfunctioning parts of a system. We are simulating malfunctioning parts of the system with different percentages such as $$10\%$$, $$25\%$$ ,etc. What I want to show is how well we predict malfunctioning parts.

For example, there are total of 100 system parts and 10 of them are malfunctioning. Our algorithm predicts 12 malfunctioning parts but in reality 8 of these predicted parts are malfunctioning. Hence, the precision of our model is $$8/12=0.66$$ and the recall is $$8/10=0.8$$. But, when the percentage of malfunctioning part is increased from 10 to 25, the precision will inevitably increase because we are dealing with another data partition for which we will have more true positives. So, precision here is not a good measure. We can still use recall for measuring the completeness of correct results. What I want to ask is should I use a metric like $$\frac{false\; positives}{false\;positives \;+\; true \;negatives}$$ to measure how many of irrelevant items are annotated as malfunctioning? Do we have a name for this metric?