Missing Data Imputation for Semiconductor Measurement Efficiency
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Solution Overview
Problem
In semiconductor memory device manufacturing, existing measurement systems face challenges in effectively obtaining and imputing missing data without measuring all components, leading to incomplete data sets and reduced efficiency in quality control processes.
Innovation Solution
A method and system for obtaining and imputing missing data by generating valid imputation data through multiple imputations using candidate data, selecting next measurement variables based on difference values, and generating average data to prioritize measurement, allowing for efficient data completion even with limited initial measurements.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If measurement values are obtained from all measurement components of the measurement object, then complete data is generated, but the measurement time and complexity increase significantly
Solution Approach 1:
The patent applies partial action by obtaining measurement values from only n measurement components (where n < z) instead of all z components. The missing data from the remaining z-n components is then imputed through multiple imputations using the obtained measurement values, generating k pieces of final imputation data. This approach achieves sufficient data completeness for quality control while significantly reducing measurement time and complexity.
2Productivity
If the number of measurements is reduced to save time, then measurement efficiency improves, but data completeness and reliability deteriorate
Solution Approach 1:
The patent introduces an intermediary process of multiple imputations to bridge the gap between reduced measurements and data completeness. The imputation process uses the obtained measurement values from n components to generate k pieces of final imputation data for the missing z-n components. This intermediary step ensures that even with reduced measurements, the imputed data maintains reliability and completeness suitable for quality control decisions.
Solution Approach 2:
The patent employs feedback by using the obtained measurement values to guide the imputation process. The measurement values from n components serve as feedback information that informs the generation of k pieces of final imputation data. This feedback mechanism ensures that the imputed data is consistent with the actual measurements, maintaining data reliability while enabling reduced measurement campaigns.
3Reliability
If multiple imputations are performed to generate valid imputation data, then data reliability improves, but computational complexity increases
Solution Approach 1:
The patent segments the imputation process into distinct steps: obtaining measurement values from n components, generating k pieces of final imputation data through multiple imputations, and selecting the next measurement variable based on difference values. This segmentation makes the computational process more manageable and systematic, reducing the overall computational complexity while maintaining data reliability through the structured multiple imputation approach.
Data Source
AI summary
A method of obtaining and imputing missing data and a measurement system having the same are disclosed. The method includes obtaining measurement values of measurement variables, among z variables corresponding to z components of a measurement object, wherein z is a natural number greater than 1, and the z variables of the measurement object include measurement variables and missing variables which are not measured, and the measurement variables are of an amount less than z; generating missing data having the measurement variables with the measurement values and the missing variables with missing values in the z components, wherein each of the missing values is predetermined value indicating that a missing variable has not been measured; generating k pieces of final imputation data having k final imputation values, by using the missing data, wherein k is a natural number greater than 1, each of the k final imputation values are in the z components, and using the missing data includes performing multiple imputations on the missing data; and generating average data having average component values in the z components, wherein each of the average component values in a component is an average value of the k final imputation values of the k pieces of final imputation data in the component, and selecting, in each of the z components, a next measurement variable, wherein a difference value between a final imputation values and an average component value, of the next measurement variable, is larger than a difference value of the missing variables.