Change Point Detection

A foundational online detection method that continuously evaluates the likelihood ratio between two hypotheses: no change versus a change has occurred. The algorithm accumulates evidence from each new sensor reading and triggers an alert when the cumulative sum exceeds a predefined threshold. This approach minimizes the average detection delay for a given false alarm rate, making it ideal for high-velocity streaming telemetry where immediate phase transition awareness is critical.

A probabilistic framework that computes the posterior distribution over run lengths—the time since the last change point—given observed data. Rather than a single point estimate, this method maintains a distribution of possible change locations, updating beliefs recursively with each new observation. Key advantages include:

• Natural uncertainty quantification around detected shifts
• Ability to incorporate prior domain knowledge about expected degradation rates
• Robust performance on noisy industrial sensor streams where hard thresholds fail

The Cumulative Sum control chart tracks the accumulated deviation of a process from a target value. When the monitored parameter shifts—such as a sudden increase in bearing vibration amplitude—the CUSUM statistic drifts upward linearly, crossing a decision boundary far faster than Shewhart charts. The algorithm is optimal for detecting sustained mean shifts and is widely deployed in manufacturing for:

• Tool wear monitoring in CNC machining
• Detecting step changes in motor current signatures
• Identifying persistent thermal runaway precursors

An offline algorithm that finds the exact optimal segmentation of a time series into homogeneous segments while operating in linear time under mild conditions. PELT uses dynamic programming with a pruning rule that discards candidate change points that can never be optimal, dramatically reducing computational cost. This method excels at retrospective analysis of historical run-to-failure datasets, enabling precise labeling of degradation phase boundaries for training supervised Remaining Useful Life models.

A non-parametric method that maps sensor data into a reproducing kernel Hilbert space and detects distributional changes using the maximum mean discrepancy statistic. This approach can identify subtle shifts in the entire probability distribution—not just the mean or variance—making it powerful for catching complex degradation patterns like changes in signal kurtosis or spectral shape. It operates without assuming any underlying parametric model, providing robustness across diverse equipment types and failure modes.

A computationally efficient divide-and-conquer strategy that repeatedly applies a single change point test to sub-segments of the time series. The algorithm first locates the most significant change point globally, then recursively searches the left and right partitions for additional shifts. While greedy and approximate, binary segmentation scales well to extremely long sensor logs and serves as a practical baseline for identifying multiple degradation stage transitions in high-frequency vibration data.

A specific type of model decay where the statistical relationship between sensor input and failure output changes over time. Unlike sensor degradation, concept drift renders the original prediction logic invalid.

• Virtual drift: Input data distribution changes, but the decision boundary remains valid
• Real drift: The posterior probability P(y|X) changes, requiring model retraining
• Change point detection algorithms are the primary defense against undetected real concept drift in production

The mathematical representation of how a system's health deteriorates over time, forming the basis for predicting Remaining Useful Life (RUL). Change point detection identifies the exact moment a system transitions from a healthy state to a degraded state.

• Exponential degradation: Failure rate increases at a constant multiplicative factor
• Paris-Erdogan model: Describes crack propagation in materials science
• Piecewise linear models: Use detected change points as knot locations for segmented regression

A composite metric that fuses multiple sensor readings into a single, normalized value representing the overall degradation state of an asset. Change point detection is applied directly to the Health Index trajectory to identify regime shifts.

• Typically normalized from 1.0 (healthy) to 0.0 (failed)
• Constructed using Principal Component Analysis (PCA) or domain-weighted fusion
• A detected change point in the Health Index triggers a transition from Condition-Based Maintenance to predictive alerting

Incomplete operational records where a machine has not yet failed, requiring specialized survival analysis techniques. Change point detection must account for censored data to avoid false positives.

• Right-censored: Asset still operational at the end of the observation window
• Interval-censored: Failure known to occur within a time window, but exact moment unknown
• Algorithms like the Kaplan-Meier estimator incorporate censored data to model survival probability without bias

The degradation of a predictive model's performance over time due to changes in the underlying data distribution or evolving equipment behavior. Change point detection serves as a drift detection mechanism.

• Covariate shift: Input feature distribution changes
• Prior probability shift: Target class distribution changes
• Monitoring the prediction error rate with CUSUM or Page-Hinkley tests identifies when a model requires retraining or replacement

The identification of rare events or observations in operational data that deviate significantly from the norm. While anomaly detection flags individual outliers, change point detection identifies sustained shifts in the generating process.

• Point anomalies: Single sensor readings outside expected bounds
• Collective anomalies: Sequences that are anomalous together but not individually
• Change point detection distinguishes a transient spike from a genuine regime change, reducing false alarms in Condition-Based Maintenance programs