Time-Series Segmentation and Anomaly Detection
Detection of data anomalies resulting from maintenance activities on semiconductor processing equipment. Time-series representation of the key indicators for equipment performance is cleaned then segmented according to sharp breaks in the data. The cleaned and segmented data is modeled, for example, by determining a linear fit for each segment. The slope and intercept of each modeled segment linear fit are compared and evaluated to identify anomalies in the data.
1 . A method for detecting anomalies resulting from maintenance activities on semiconductor equipment, comprising:
receiving a time-series dataset corresponding to at least one measured parameter of the semiconductor equipment;
cleaning the dataset;
segmenting the cleaned dataset;
statistical modeling of the segmented cleaned dataset; and
identifying anomalies in the dataset based on the statistical modeling of the segmented cleaned dataset.
2 . The method of claim 1 , further comprising taking corrective action to repair, replace or recalibrate the semiconductor equipment.
3 . The method of claim 1 , the dataset comprising at least one statistical indicator identified as useful in evaluating performance of the semiconductor equipment.
4 . The method of claim 1 , the cleaning step further comprising:
removing outliers from the dataset; and
reducing variation in the dataset.
5 . The method of claim 4 , the step of removing outliers further comprising, for each of a plurality of data points in the dataset:
determine a linear fit around the data point;
calculate the mean value of the linear fit;
calculate the difference between the mean value of the linear fit and the data point; and
remove the data point from the dataset if the difference exceeds a threshold.
6 . The method of claim 5 , further comprising replacing the removed data point in the dataset with the mean value.
7 . The method of claim 4 , the step of removing outliers further comprising, for each of a plurality of data points in the dataset:
define a neighborhood of points adjacent to the data point;
calculate the mean value of the neighborhood of points;
evaluate the difference between the mean value of the neighborhood of points and the data point; and
remove the data point from the dataset if the evaluation of the difference indicates that the data point is anomalous.
8 . The method of claim 4 , the step of reducing variation further comprising bootstrapping the dataset to approximate a distribution of the dataset.
9 . The method of claim 1 , the segmentation step further comprising evaluating a distribution of data points in the dataset for a plurality of segments of time.
10 . The method of claim 9 , the segmentation step implemented using a change-point detection algorithm.
11 . The method of claim 1 , the segmentation step further comprising evaluating how a distribution of data points in the dataset varies over time.
12 . The method of claim 1 , further comprising;
for each segment identified in the segmentation step, determine a linear fit for a plurality of data points in the segment;
determine a slope and an intercept corresponding to each linear fit; and
evaluate differences in the determined slopes and intercepts.
13 . A method for detecting anomalies resulting from maintenance activities on semiconductor equipment, comprising:
receiving a time-series dataset having a plurality of data points corresponding to at least one measured parameter of the semiconductor equipment;
reducing noise in the dataset;
identifying a plurality of segments in the dataset on the basis of a plurality of discernable shifts in the data points;
determining from the plurality of segments trends in the data points based on the segments; and
determining whether the trends in the data points are expected or anomalous.
14 . The method of claim 13 , the step of determining whether the trends in the data points are expected or anomalous is implemented in a change-point detection algorithm.
15 . The method of claim 13 , the step of determining whether the trends in the data points are expected or anomalous is implemented in a rolling window detection algorithm.
16 . The method of claim 13 , further comprising:
removing outliers from the dataset; and
reducing variation in the dataset.
17 . The method of claim 16 , the step of removing outliers further comprising, for each of a plurality of data points in the dataset:
defining a neighborhood of points adjacent to the data point;
calculating the mean value of the neighborhood of points;
evaluating the difference between the mean value of the neighborhood of points and the data point; and
removing the data point from the dataset if the evaluation of the difference indicates that the data point is anomalous.