System and method for partitioning a real-valued attribute exhibiting windowed data characteristics

• US 6,336,106 B1
• Filed: 02/19/1998
• Issued: 01/01/2002
• Est. Priority Date: 02/15/1994
• Status: Expired due to Term

• Current Assignee: LSC Communications LLC (LSC Communications, Inc.)
• Original Assignee: RR Donnelley & Sons Company
• Inventors: Evans, Robert
• Primary Examiner(s): Chaki, Kakali
• Assistant Examiner(s): STARKS, WILBERT L
• Application Number:
  US09/026,267
• Time in Patent Office: 1,412 Days
• Field of Search: 706/12, 704/224, 342/64, 342/383
• US Class Current: 706/12
• CPC Class Codes: G06F 11/25 Testing of logic operation, e.g. by logic analysers
• CPC Class Codes: G06N 5/025 Extracting rules from data

Abstract

A system and method are disclosed for partitioning a real-value windowed attribute into ranges, wherein the values within each range generally correspond to a particular class of results associated with runs of a process. The system and method determines a low range having attribute values generally corresponding to a first class, a middle range having attribute values generally corresponding to a second class, and an upper range having attribute values generally corresponding to the first class. The system and method may be used in a system that produces an induction tree useful in developing an indication of a cause of a particular result of a process from values associated with at least one real-valued, windowed attribute that arises during the runs of the process.

Claims

1. A method of dividing a real-valued process attribute representative of a characteristic of a production process and having values associated with a first class representative of a first result of the production process generally windowed by values associated with a second class representative of a second result of the production process into ranges, the method comprising:

a step for separating the values of the real-valued process attribute into a first set if the values are associated with the first class and into a second set if the values are associated with the second class;

a step for calculating a statistical property of the second set;

a step for defining a first subset as the values in the first set to one side of the statistical property of the second set and a second subset to include values of the second set; and

a step for repeating;

(a) a step for calculating a statistical property of the first subset and a statistical property of the second subset; and

(b) a step for removing values from the first subset and the second subset based on the calculated statistical properties of the first and second subsets; and

a step for determining a first range breakpoint between the first and second subsets from one or more of the statistical properties of the first subset and the second subset calculated in step (a), wherein the first range breakpoint generally represents a division between values of the real-valued process attribute corresponding to the first result of the production process and values of the real-valued process attribute corresponding to the second result of the production process.

2. The method of claim 1, wherein the step for defining defines the first subset to include the values in the first set below the statistical property of the second set and wherein the steps (a) and (b) are repeated until the statistical property of the first subset is greater than or equal to the statistical property of the second subset.

3. The method of claim 1, wherein the step for defining defines the first subset to include the values in the first set above the statistical property of the second set and wherein steps (a) and (b) are repeated until the statistical property of the first subset is less than or equal to the statistical property of the second subset.

4. The method of claim 1, wherein the step for defining defines the first subset to include the values in the first set below the statistical property of the second set the method further including:

a step for defining a third subset as the values in the first set above the statistical property of the second set and a fourth subset to include values of the second set;

a step for repeating;

(c) a step for calculating a statistical property of the third subset and a statistical property of the fourth subset; and

(d) a step for removing values from the third subset and the fourth subset based on the calculated statistical properties of the third and fourth subsets; and

a step for determining a second range breakpoint from one or more of the statistical properties of the third subset and the fourth subset calculated in step (c), wherein the second range breakpoint generally represents a division between values of the real-valued process attribute corresponding to the first result of the production process and values of the real-valued process attribute corresponding to the second result of the production process.

5. The method of claim 4, wherein the step for determining the first range breakpoint includes a step for setting the first range breakpoint equal to the statistical property of the first subset and the step for determining the second range breakpoint includes a step for setting the second range breakpoint equal to the statistical property of the fourth subset.

6. The method of claim 4, wherein the step for determining the first range breakpoint includes a step for setting the first range breakpoint equal to the statistical property of the second subset and the step for determining the second range breakpoint includes a step for setting the second range breakpoint equal to the statistical property of the third subset.

7. The method of claim 1, wherein the step for determining the first range breakpoint includes a step for calculating the first range breakpoint as a combination of the statistical properties of the first and second subsets.

8. A system for use in developing an indication of a cause of a particular result of a production process from values associated with attributes arising during runs of the production process, wherein the runs during which the particular result occurred are in a first class and the runs during which the particular result did not occur are in a second class, and at least one of the attributes is a real-valued attribute having values associated with one of the classes generally windowed by values associated with the other one of the classes, comprising:

a data entry device for permitting a user to enter data indicating the attribute values and the class associated with each of the attribute values;

a memory for storing the data indicating the attribute values and the class associated with each of the attribute values;

a processing unit including a second memory that stores a computer-implementable routine that performs;

a step for separating the values of the real-valued attribute into first and second sets based on the class associated with each of the values;

a step for calculating a statistical property of the second set;

a step for defining a first subset as the values in the first set to one side of the statistical property of the second set and a second subset to include values of the second set;

a step for repeating;

(a) a step for calculating a statistical property of the first subset and a statistical property of the second subset; and

(b) a step for removing values from the first subset and the second subset based on the calculated statistical properties of the first and second subsets; and

a step for determining a first range breakpoint from one or more of the statistical properties of the first and second subsets calculated in step (a), wherein the first range breakpoint generally represents a division between values corresponding to runs of the production process during which a particular result occurred and values corresponding to runs of the production process during which the particular result did not occur.

9. The system of claim 8, wherein the computer-implementable routine performs the step for defining the first subset to include the values in the first set below the statistical property of the second set, wherein the computer-implementable routine further performs:

a step for defining a third subset to include the values in the first set above the statistical property of the second set and a fourth subset to include the values of the second set;

a step for repeating;

(c) a step for calculating a statistical property of the third subset and a statistical property of the fourth subset; and

(d) a step for removing values from the third subset and the fourth subset based on the calculated statistical properties of the third and fourth subsets; and

a step for determining a second range breakpoint from one or more of the statistical properties of the third subset and the fourth subsets calculated in step (c), wherein the second range breakpoint generally represents a division between values corresponding to runs of the production process during which a particular result occurred and values corresponding to runs of the production process during which the particular result did not occur.

10. The system of claim 9, wherein the computer-implementable routine performs the step for determining the first range breakpoint by setting the first range breakpoint equal to the statistical property of the first subset and the performs the step for determining the second range breakpoint by setting the second range breakpoint equal to the statistical property of the fourth subset.

11. The system of claim 8, wherein the computer-implementable routine performs a step for determining if the first real-valued attribute has values that are windowed.

12. The system of claim 11, wherein the step for determining if the real-valued attribute has values that are windowed includes:

a step for creating a fifth subset to include the values of the first set below the statistical property of the second set;

a step for creating a sixth subset to include the values of the first set above the statistical property of the second set;

a step for determining a statistical property of the fifth subset and of the sixth subset; and

a step for identifying that the values of the real-valued attribute are windowed if the statistical property of the fifth subset is less than the statistical property of the second set by a first amount and the statistical property of the sixth subset is greater than the statistical property of the second set by a second amount.

13. A method of dividing values of a real-valued process attribute for a number of runs of a production process into ranges having classes generally associated therewith, the method comprising:

a) a step for creating a first data set that contains the values of the real-valued process attribute for the runs of the production process corresponding to a first class representing runs during which a particular result occurred;

b) a step for creating a second data set that contains the values of the real-valued process attribute for the runs of the production process corresponding to a second class representing runs during which the particular result did not occur;

c) a step for calculating a first statistical property that is a statistical property of the second data set;

d) a step for creating a first subset that contains the values in the first data set that are less than the first statistical property;

e) a step for creating a second subset that contains the values of the second data set;

f) a step for calculating a second statistical property that is a statistical property of the first subset and a third statistical property that is a statistical property of the second subset;

g) a step for saving the second and third statistical properties;

h) a step for eliminating the data values in the first subset that are lower than the second statistical property and eliminating the data values in the second subset that are higher than the third statistical property;

i) a step for recalculating the second statistical property as a statistical property of the first subset and the third statistical property as a statistical property of the second subset;

j) a step for determining a first breakpoint from one or more of the second and third statistical properties saved in step (g) if the second statistical property of step (i) is greater than or equal to the third statistical property of step (i), wherein the first breakpoint generally represents a division between values corresponding to runs of the production process during which the particular result occurred and values corresponding to runs of the production process during which the particular result did not occur;

k) a step for repeating steps g) through j) until the second statistical property is greater than or equal to the third statistical property;

l) a step for creating a third subset that contains the values of the second data set and a fourth subset that contains the values of the first data set that are greater than the first statistical property;

m) a step for calculating a fourth statistical property that is a statistical property of the third subset and a fifth statistical property that is a statistical property of the fourth subset;

n) a step for saving the fourth and fifth statistical properties;

o) a step for eliminating the values in the third subset that are lower than the fourth statistical property and eliminating the values in the fourth subset that are higher than the fifth statistical property

p) a step for recalculating the fourth statistical property as a statistical property of the third subset and the fifth statistical property as a statistical property of the fourth subset;

q) a step for setting a second breakpoint based on one or more of the fourth or fifth statistical properties saved in step (n) if the fourth statistical property of step (p) is greater than or equal to the fifth statistical property of step (p), wherein the second breakpoint generally represents a division between values corresponding to runs of the production process during which the particular result occurred and values corresponding to runs of the production process during which the particular result did not occur;

r) a step for repeating steps n) through q) until the fourth statistical property is greater than or equal to the fifth statistical property; and

s) a step for using the first and second breakpoints to divide the values of the attribute into a set of ranges.

14. The method of claim 13, wherein the second statistical property, the third statistical property, the fourth statistical property, and the fifth statistical property, is each a median.

15. The method of claim 13, wherein the second statistical property, the third statistical property, the fourth statistical property, and the fifth statistical property, is each a mean.

16. The method of claim 13, wherein the values for the real-valued attribute are between a minimum value and a maximum value and wherein the set of ranges comprises:

a first range including the values for the real-valued attribute from the minimum value through the first breakpoint;

a second range including the values for the real-valued attribute from the first breakpoint through the second breakpoint; and

a third range including the values for the real-valued attribute from the second breakpoint to the maximum value.

17. The method of claim 13, further including a step or using the set of ranges to create an induction tree that uses the real-valued attribute.

18. A system for use in developing an indication of a cause of a particular result of a production process from values associated with attributes arising during runs of the production process, wherein the runs during which the particular result occurred are in a first class and the runs during which the particular result did not occur are in a second class, and at least one of the attributes is a real-valued attribute having values associated with one of the classes generally windowed by values associated with the other one of the classes, the system comprising:

a data entry device for permitting a user to enter data indicating the attribute values and the class associated with each of the attribute values;

a memory for storing the data indicating the attribute values and the class associated with each of the attribute values;

a) a means for creating a first data set that contains the values of the real-valued attribute for the runs of the process corresponding to the first class;

b) a means for creating a second data set that contains the values of the real-valued attribute for the runs of the process corresponding to the second class;

c) a means for calculating a first statistical property that is a statistical property of the second data set;

d) a means for creating a first subset that contains the values in the first data set that are less than the first statistical property;

e) a means for creating a second subset that contains the values of the second data set;

f) a means for calculating a second statistical property that is a statistical property of the first subset and a third statistical property that is a statistical property of the second subset;

g) a means for saving the second and third statistical properties;

h) a means for eliminating the data values in the first subset that are lower than the second statistical property and eliminating the data values in the second subset that are higher than the third statistical property;

i) a means for recalculating the second statistical property as a statistical property of the first subset and the third statistical property as a statistical property of the second subset;

j) a means for determining a first breakpoint from one or more of the second and third statistical properties saved in step (g) if the second statistical property of step (i) is greater than or equal to the third statistical property of step (i);

k) a means for executing the means (g) through (j) until the second statistical property is greater than or equal to the third statistical property;

l) a means for creating a third subset that contains the values of the second data set and a fourth subset that contains the values of the first data set that are greater than the first statistical property,

m) a means for calculating a fourth statistical property that is a statistical property of the third subset and a fifth statistical property that is a statistical property of the fourth subset;

n) a means for saving the fourth and fifth statistical properties;

o) a means for eliminating the values in the third subset that are lower than the fourth statistical property and eliminating the values in the fourth subset that are higher than the fifth statistical property;

p) a means for recalculating the fourth statistical property as a statistical property of the third subset and the fifth statistical property as a statistical property of the fourth subset;

q) a means for setting a second breakpoint based on one or more of the fourth or fifth statistical properties saved by the means (n) if the fourth statistical property of the means (p) is greater than or equal to the fifth statistical property of the means (p);

r) a means for repeating the means (n) through (q) until the fourth statistical property is greater than or equal to the fifth statistical property; and

s) a means for using the first and second breakpoints to divide the values of the attribute into a set of ranges, wherein the first and second breakpoints generally represent divisions between values corresponding to runs of the production process during which the particular result occurred and values corresponding to runs of the production process during which the particular result did not occur.

19. The system of claim 18, wherein the second statistical property, the third statistical property, the fourth statistical property, and the fifth statistical property, is each a median.

20. The system of claim 18, wherein the second statistical property, the third statistical property, the fourth statistical property, and the fifth statistical property, is each a mean.

21. The system of claim 18, further including a means for using the set of ranges to create an induction tree that uses the real-valued attribute.

22. The system of claim 18, further including a means for determining if an attribute has values that are windowed.

23. The system of claim 22, wherein the means for of determining if the attribute has values that are window includes:

a means for creating a fifth subset to include the values of the first set below the statistical property of the second set;

a means for creating a sixth subset to include the values of the first set above the statistical property of the second set;

a means for determining a statistical property of the fifth subset and of the sixth subset; and

a means for identifying that the values of the attribute are windowed if the statistical property of the fifth subset is less than the statistical property of the second set by a first amount and the statistical property of the sixth subset is greater than the statistical property of the second set by a second amount.