The best option for choosing a model that prioritizes detection while ensuring that more than 50% of the maintenance jobs triggered by the model address an imminent machine failure is to choose the model with the highest recall where precision is greater than 0.5. This option has the following advantages:

It maximizes the recall, which is the proportion of actual failures that are correctly predicted by the model. Recall is also known as sensitivity or true positive rate (TPR), and it is calculated as:

mathrmRecall=fracmathrmTPmathrmTP+mathrmFN

where TP is the number of true positives (actual failures that are predicted as failures) and FN is the number of false negatives (actual failures that are predicted as non-failures). By maximizing the recall, the model can reduce the number of false negatives, which are the most costly and undesirable outcomes for the predictive maintenance use case, as they represent missed failures that can lead to machine breakdown and downtime.

It constrains the precision, which is the proportion of predicted failures that are actual failures. Precision is also known as positive predictive value (PPV), and it is calculated as:

mathrmPrecision=fracmathrmTPmathrmTP+mathrmFP

where FP is the number of false positives (actual non-failures that are predicted as failures). By constraining the precision to be greater than 0.5, the model can ensure that more than 50% of the maintenance jobs triggered by the model address an imminent machine failure, which can avoid unnecessary or wasteful maintenance costs.

The other options are less optimal for the following reasons:

Option A: Choosing the model with the highest area under the receiver operating characteristic curve (AUC ROC) and precision greater than 0.5 may not prioritize detection, as the AUC ROC does not directly measure the recall. The AUC ROC is a summary metric that evaluates the overall performance of a binary classifier across all possible thresholds. The ROC curve plots the TPR (recall) against the false positive rate (FPR), which is the proportion of actual non-failures that are incorrectly predicted by the model. The AUC ROC is the area under the ROC curve, and it ranges from 0 to 1, where 1 represents a perfect classifier. However, choosing the model with the highest AUC ROC may not maximize the recall, as the AUC ROC is influenced by both the TPR and the FPR, and it does not account for the precision or the specificity (the proportion of actual non-failures that are correctly predicted by the model).

Option B: Choosing the model with the lowest root mean squared error (RMSE) and recall greater than 0.5 may not prioritize detection, as the RMSE is not a suitable metric for binary classification. The RMSE is a regression metric that measures the average magnitude of the error between the predicted and the actual values. The RMSE is calculated as:

mathrmRMSE=sqrtfrac1nsumi=1n​(yi​−hatyi​)2

where yi​ is the actual value, hatyi​ is the predicted value, and n is the number of observations. However, choosing the model with the lowest RMSE may not optimize the detection of failures, as the RMSE is sensitive to outliers and does not account for the class imbalance or the cost of misclassification.

Option D: Choosing the model with the highest precision where recall is greater than 0.5 may not prioritize detection, as the precision may not be the most important metric for the predictive maintenance use case. The precision measures the accuracy of the positive predictions, but it does not reflect the sensitivity or the coverage of the model. By choosing the model with the highest precision, the model may sacrifice the recall, which is the proportion of actual failures that are correctly predicted by the model. This may increase the number of false negatives, which are the most costly and undesirable outcomes for the predictive maintenance use case, as they represent missed failures that can lead to machine breakdown and downtime.

References:

Evaluation Metrics (Classifiers) - Stanford University

Evaluation of binary classifiers - Wikipedia

Predictive Maintenance: The greatest benefits and smart use cases