Multivariate Unusualness Detection for Correlated Quality Data
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Solution Overview
Problem
Current quality control methods, such as univariate and bivariate methods, often lead to false alarms and reject too many components, failing to guarantee zero defects, especially when dealing with a large number of measurements, and are not applicable when the number of measurements exceeds the number of individuals or when there is correlation between variables, which is common in industrial contexts.
Innovation Solution
A method for determining the level of unusualness of individuals using pre-processing, multivariate unusualness index calculation, and identification of unusual individuals through standardization, transformation of indices, and grouping, allowing for real-time detection even when the number of measurements exceeds the number of individuals and accounting for correlations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If univariate or bivariate statistical methods are used to detect unusual individuals, then the detection of potentially defective components is improved, but the number of false alarms increases drastically with the number of measurements
Solution Approach 1:
The patent segments the detection process into multiple stages: first applying univariate/bivariate methods to identify suspicious individuals, then applying multivariate analysis specifically to those segmented cases. This segmentation allows the use of simpler methods for initial screening while reserving the more complex multivariate analysis for cases where it is most needed, thereby reducing overall false alarms while maintaining detection accuracy.
Solution Approach 2:
The patent transitions from univariate/bivariate analysis to multivariate analysis by adding dimensional complexity. When the number of measurements exceeds the number of individuals or when correlations exist between variables, the method moves to multivariate space to detect unusual patterns that cannot be identified in lower dimensions, thus improving reliability without being constrained by the limitations of simpler methods.
2Productivity
If statistical limits are selected permissively to limit false alarms, then the cost related to detection is reduced, but the risk of not eliminating all potentially defective components increases
Solution Approach 1:
The patent employs dynamic threshold adjustment where statistical limits are not fixed but adapt based on the specific case. For individuals flagged by univariate/bivariate methods, the multivariate analysis dynamically adjusts the significance level and thresholds based on the data characteristics, allowing more stringent limits when needed and more permissive limits when appropriate, thus balancing productivity and reliability.
Solution Approach 2:
The method incorporates feedback loops where the results of multivariate analysis feed back into the detection system. By continuously learning from detected cases and adjusting statistical parameters accordingly, the system optimizes the balance between false alarm reduction and defect elimination, improving both productivity and reliability over time through adaptive feedback mechanisms.
3Reliability
If the number of measurements increases to improve detection coverage, then the ability to detect latent defects is improved, but the applicability of current methods decreases when measurements exceed individuals or variables are correlated
Solution Approach 1:
The patent explicitly addresses the scenario where the number of measurements p exceeds the number of individuals n by transitioning to multivariate analysis that can handle high-dimensional data. The method uses techniques such as principal component analysis and handles correlated variables through covariance-based approaches, enabling detection coverage to improve with increased measurements without losing method applicability.
Solution Approach 2:
The patent changes key parameters of the statistical methods to adapt to different data conditions. When measurements exceed individuals or correlations are present, the method adjusts the statistical model parameters, switching from traditional univariate approaches to multivariate frameworks with appropriate assumptions about data structure, thereby maintaining versatility while improving detection coverage.
4Reliability
If zero-defect objective is pursued using univariate or bivariate methods, then the elimination of good parts is increased, but the guarantee of zero defects is not achieved
Solution Approach 1:
The patent segments the quality control process into multiple analytical stages, applying univariate/bivariate methods first to identify candidates for further inspection, then applying multivariate analysis to those specific cases. This segmentation ensures that good parts are not eliminated in the initial screening since multivariate analysis provides the definitive zero-defect guarantee only when applied to suspicious cases, thereby minimizing production loss while pursuing the zero-defect objective.
Solution Approach 2:
The patent applies the more rigorous multivariate analysis partially, only to individuals flagged by preliminary univariate/bivariate screening, rather than applying it excessively to all individuals. This partial application of the more stringent method achieves the zero-defect guarantee for the screened population while avoiding the excessive rejection of good parts that would occur if the stringent method were applied universally, thus balancing production loss with defect elimination.
Data Source
AI summary
A method for determining the level of unusualness of individuals, in particular in order to statistically detect unusual individuals in a set of previously gathered data resulting from measurements of parameters of individuals taken by a plurality of measuring systems. The data is pre-processed, and a multivariate unusualness index is determined. The index being transformed by a function so as to be between 0 and 1, on the set of measurements for each individual based on the preprocessed data. Unusual individuals are then identified.