Perturbation Method for Low-Resolution Measurement Normality Testing
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Solution Overview
Problem
Current systems face challenges in accurately testing the normality of data with low-resolution measurements, often leading to false rejections of distribution assumptions due to measurement rounding or truncation, which is costly and time-consuming, especially in sensitive applications like medical device testing.
Innovation Solution
A method that reintroduces variation into low-resolution measurements by iteratively computing perturbed values until a termination criterion is met, allowing for higher resolution and subsequent distribution testing using methods like the Anderson-Darling test to assess normality.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If distribution testing is performed directly on low-resolution measurements, then the testing process is simple and fast, but false rejections of distribution assumptions occur due to measurement rounding
Solution Approach 1:
The patent applies preliminary action by performing perturbation on the low-resolution measurements before conducting distribution testing. The method generates perturbed values that reintroduce variation lost due to rounding, then uses these perturbed values for the actual distribution testing. This preliminary perturbation step prevents false rejections while maintaining the simplicity of the overall process.
2Measurement precision
If higher resolution measurements are used, then measurement precision improves, but measurement cost and time increase
Solution Approach 1:
The patent uses copying by creating perturbed values that simulate what the measurements would look like at higher resolution. Instead of actually taking higher resolution measurements, the method copies the essential variation information through mathematical perturbation based on the known rounding interval. This provides the benefits of high-resolution analysis without the cost and time of actual high-resolution measurement.
3Reliability
If iterative perturbation is performed to correct low-resolution measurements, then distribution testing accuracy improves, but computational time increases
Solution Approach 1:
The patent applies partial action by performing a limited number of perturbation iterations rather than exhaustive computation. The method generates perturbed values and performs distribution testing, using just enough perturbation to reintroduce the essential variation information needed to prevent false rejections. This avoids excessive computational time while achieving the reliability improvement.
Data Source
AI summary
Methods and systems to correct low-resolution measurements corresponding to unobservable high-resolution measurements by introducing variation in the plurality of low-resolution measurements to obtain perturbed values for the low-resolution measurements. The perturbed values have a higher resolution than another resolution of the low-resolution measurements. A distribution test is performed on the perturbed values.