SHapley Additive exPlanations (SHAP)

The sum of all feature attributions must equal the difference between the model's prediction for a specific instance and the average baseline prediction.

• Additivity: f(x) = φ₀ + Σᵢ φᵢ where φ₀ is the expected model output and φᵢ is the SHAP value for feature i
• Ensures the explanation is faithful to the original model output for that exact data point
• Matches the efficiency property in cooperative game theory, where the total payout equals the coalition's value

A feature that is absent from the input must receive an attribution of exactly zero.

• Structural zero: If x'ᵢ = 0 (feature is missing in the simplified input), then φᵢ = 0
• Prevents spurious attributions to features that were not observed
• Critical for handling sparse feature vectors and missing sensor readings in industrial telemetry
• Ensures the explanation does not invent importance for non-existent inputs

If a model changes so that a feature's marginal contribution increases or stays the same regardless of other features, that feature's attribution must not decrease.

• Monotonicity guarantee: Changing the model to rely more on a feature cannot reduce its SHAP value
• Prevents attribution paradoxes where a more important feature receives less credit
• Derived directly from the Shapley value's monotonicity axiom in cooperative game theory
• Ensures explanations remain logically coherent across model iterations

SHAP is the only additive feature attribution method that simultaneously satisfies Local Accuracy, Missingness, and Consistency.

• Proven by Lundberg and Lee (2017) as a unification of LIME, DeepLIFT, and Shapley values
• Any method violating one of these properties introduces logical inconsistencies in explanations
• Provides the theoretical guarantee that SHAP attributions are the unique fair distribution of credit among input features
• Establishes SHAP as the gold standard for model-agnostic interpretability in high-stakes applications like predictive maintenance

A broader concept quantifying how much each input variable contributes to a model's predictive power. SHAP provides a unified measure of feature importance grounded in cooperative game theory, resolving inconsistencies found in other methods like permutation importance or Gini impurity-based importance from tree models. In a predictive maintenance context, SHAP-derived feature importance can reveal that vibration RMS is 3x more critical than ambient temperature for predicting bearing failure, guiding sensor investment and engineering focus.

The phenomenon where the statistical relationship between sensor inputs and failure outputs changes over time, rendering the original prediction logic invalid. SHAP is a critical diagnostic tool for detecting concept drift:

• Monitor SHAP value distributions over time for each feature
• A sudden shift in a feature's attribution pattern signals that the underlying physics of degradation have changed
• For example, if oil viscosity suddenly becomes the dominant SHAP contributor when it previously had negligible impact, this may indicate a new failure mode or a change in lubricant supplier This allows maintenance engineers to trigger model retraining before prediction accuracy degrades.

A supervised learning task that categorizes the specific type of equipment malfunction—such as bearing wear, shaft misalignment, or cavitation—from sensor signatures. SHAP enhances failure mode classification by:

• Explaining why a particular failure mode was predicted over alternatives
• Highlighting which frequency bands in an FFT spectrum most strongly indicate a specific fault type
• Providing per-class SHAP values that decompose the model's confidence across multiple potential failure modes This granular explainability is essential for directing maintenance crews to the exact root cause rather than a generic alert.

The most advanced stage of analytics maturity, where systems not only predict failure but autonomously recommend specific repair actions and optimal scheduling windows. SHAP bridges the gap between predictive and prescriptive maintenance by:

• Justifying the recommended action with transparent feature attributions
• Enabling what-if analysis: adjusting a feature value and observing the SHAP-driven change in failure probability
• Building operator trust in automated recommendations by showing exactly which sensor readings drove the prescription For example, a SHAP waterfall plot can demonstrate that reducing spindle load by 15% will extend RUL by an estimated 120 operating hours.