Methods and apparatus for data analysis
Methods and apparatus for data analysis according to various aspects of the present invention identify statistical outliers in data, such as test data for components. The outliers may be identified and categorized according to the distribution of the data. In addition, outliers may be identified according to multiple parameters, such as spatial relationships, variations in the test data, and correlations to other test data.
1. A semiconductor test data analysis system for identifying outliers in semiconductor test data, comprising:
a memory configured to store the test data; and
a processor connected to the memory, wherein the processor is configured to:
retrieve the test data from memory;
compare the test data to an upper outlier threshold and a lower outlier threshold, wherein the upper outlier threshold and the lower outlier threshold are derived from a median of a frequency distribution of the test data; and
determine whether the test data include outliers according to the comparison of the test data to the upper outlier threshold and the lower outlier threshold.
2. A semiconductor test data analysis system according to claim 1 , wherein:
the upper outlier threshold is derived from a third quartile mark; and
the lower outlier threshold is derived from a first quartile mark.
3. A semiconductor test data analysis system according to claim 1 , wherein the thresholds are asymmetric relative to the median.
4. A semiconductor test data analysis system according to claim 1 , wherein the processor is configured to adjust the thresholds according to a slope of the frequency distribution.
5. A semiconductor test data analysis system according to claim 1 , wherein the processor is configured to categorize the outliers according to a magnitude of the outliers.
6. A semiconductor test data analysis system according to claim 1 , wherein the processor is configured to assign categories to the outliers according to a range between at least one of the thresholds and an edge of the distribution.
7. A semiconductor test data analysis system according to claim 1 , wherein the processor is configured to determine whether the test data include outliers according to a correlation of data corresponding to at least two parameters.
8. A non-transitory computer readable medium containing computer instructions stored therein for causing a computer processor to perform a method of identifying outliers in semiconductor test data, comprising:
establishing an upper outlier threshold and a lower outlier threshold according to the test data, wherein the upper outlier threshold and the lower outlier threshold are derived from a median of a frequency distribution of the test data;
comparing the test data to the upper outlier threshold and the lower outlier threshold; and
identifying outliers in the test data according to the comparison of the test data to the upper outlier threshold and the lower outlier threshold.
9. A non-transitory computer readable medium containing computer instructions stored therein for causing a computer processor to perform a method of identifying outliers according to claim 8 , wherein:
establishing the upper outlier threshold comprises identifying a third quartile mark; and
establishing the lower outlier threshold comprises identifying a first quartile mark.
10. A non-transitory computer readable medium containing computer instructions stored therein for causing a computer processor to perform a method of identifying outliers according to claim 8 , wherein the thresholds are asymmetric relative to the median.
11. A non-transitory computer readable medium containing computer instructions stored therein for causing a computer processor to perform a method of identifying outliers according to claim 8 , wherein establishing the upper outlier threshold and the lower outlier threshold includes adjusting the thresholds according to a slope of the frequency distribution.
12. A non-transitory computer readable medium containing computer instructions stored therein for causing a computer processor to perform a method of identifying outliers according to claim 8 , further comprising categorizing the outliers according to a magnitude of the outliers.
13. A non-transitory computer readable medium containing computer instructions stored therein for causing a computer processor to perform a method of identifying outliers according to claim 8 , further comprising assigning categories to the outliers according to a range between at least one of the thresholds and an edge of the distribution.
14. A non-transitory computer readable medium containing computer instructions stored therein for causing a computer processor to perform a method of identifying outliers according to claim 8 , further comprising determining whether the test data include outliers according to a correlation of data corresponding to at least two parameters.
15. A medium storing instructions for causing a computer to execute a process, wherein the process comprises:
retrieving a set of semiconductor test data from a memory;
establishing an upper outlier threshold and a lower outlier threshold, wherein the upper outlier threshold and the lower outlier threshold are derived from a median of a frequency distribution of the test data;
comparing the test data to the upper outlier threshold and the lower outlier threshold; and
determining whether the test data include outliers according to the comparison of the test data to the upper outlier threshold and the lower outlier threshold.
16. A medium according to claim 15 , wherein:
establishing the upper outlier threshold comprises identifying a third quartile mark; and
establishing the upper outlier threshold comprises identifying a first quartile mark.
17. A medium according to claim 15 , wherein the thresholds are asymmetric relative to the median.
18. A medium according to claim 15 , wherein establishing the upper outlier threshold and the lower outlier threshold includes adjusting the thresholds according to a slope of the frequency distribution.
19. A medium according to claim 15 , wherein the process further comprises categorizing the outliers according to a magnitude of the outliers.
20. A medium according to claim 15 , wherein the process further comprises assigning categories to the outliers according to a range between at least one of the thresholds and an edge of the distribution.
21. A medium according to claim 15 , wherein the process further comprises determining whether the test data include outliers according to a correlation of data corresponding to at least two parameters.