CA2474812A1 - Manufacturing design and process analysis system - Google Patents

Manufacturing design and process analysis system Download PDF

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Publication number
CA2474812A1
CA2474812A1 CA002474812A CA2474812A CA2474812A1 CA 2474812 A1 CA2474812 A1 CA 2474812A1 CA 002474812 A CA002474812 A CA 002474812A CA 2474812 A CA2474812 A CA 2474812A CA 2474812 A1 CA2474812 A1 CA 2474812A1
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characteristic
article
predictor
value
remaining
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CA2474812C (en
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Steve W. Tuszynski
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    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B1/00—Comparing elements, i.e. elements for effecting comparison directly or indirectly between a desired value and existing or anticipated values
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B19/00—Programme-control systems
    • G05B19/02—Programme-control systems electric
    • G05B19/418—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS], computer integrated manufacturing [CIM]
    • G05B19/41865—Total factory control, i.e. centrally controlling a plurality of machines, e.g. direct or distributed numerical control [DNC], flexible manufacturing systems [FMS], integrated manufacturing systems [IMS], computer integrated manufacturing [CIM] characterised by job scheduling, process planning, material flow
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B15/00—Systems controlled by a computer
    • G05B15/02—Systems controlled by a computer electric
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G—PHYSICS
    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B2219/00—Program-control systems
    • G05B2219/30—Nc systems
    • G05B2219/32—Operator till task planning
    • G05B2219/32058—Execute program as function of deviation from predicted state, result
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/08—Probabilistic or stochastic CAD
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2113/00—Details relating to the application field
    • G06F2113/22—Moulding
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
    • Y02P90/00—Enabling technologies with a potential contribution to greenhouse gas [GHG] emissions mitigation
    • Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]

Abstract

Methods, and system that facilitate the design, production and/or measuremen ts tasks associated with manufacturing and other processes. In one embodiment, the present invention relates to decision making and logic structures, implemented in a computer software application, facilitating all phases of t he design, development, tooling, pre-production, qualification, certification, and production process of any part or other article that is produced to specification. In one embodiment, the present invention provides knowledge o f how the multiple characteristics of a given process output are related to ea ch other, to specification limits and to pre-process inputs.

Claims (130)

1. A method facilitating design and manufacturing processes, the method comprising receiving a plurality of article characteristic values associated with a set of articles having a range of variation as to a plurality of article characteristics;
selecting a predictor characteristic from the plurality of article characteristics; and, determining the regression model(s) between the predictor characteristic and at least one of the remaining article characteristics in the plurality of article characteristics.
2. The method of claim 1 further comprising receiving a target value for the predictor characteristic and a target value for at least one remaining article characteristic;
determining the intersection of the target value for the predictor characteristic and the target value of a first remaining article characteristic relative to the regression model between the predictor characteristic and the first remaining article characteristic.
3. The method of claim 1 further comprising determining the respective upper and lower prediction intervals associated with the regression model(s) between the predictor characteristic and at least one of the remaining article characteristics.
4. The method of claim 2 further comprising determining the respective upper and lower prediction intervals associated with the regression model(s) between the predictor characteristic and at least one of the remaining article characteristics.
5. The method of claim of 4 further comprising receiving lower and upper specification limits for the predictor characteristic and at least one of the remaining article characteristics;
locating the lower and upper specification limits associated with said at least one remaining article characteristic;

locating the upper and lower specification limits associated with the predictor characteristic.
6. The method of claim 1 further comprising receiving lower and upper specification limits for at least one of the remaining article characteristics;
locating the lower and upper specification limits associated with at least one remaining article characteristic relative to the regression model between the predictor characteristic and said at least one remaining article characteristic.
7. The method of claim 6 further comprising determining the value of the predictor characteristic at which the corresponding regression model intersects the upper specification limit for at least one remaining article characteristic.
8. The method of claim 6 or 7 further comprising determining the value of the predictor characteristic at which the corresponding regression model intersects the lower specification limit for at least one remaining article characteristic.
9. The method of claim 3 further comprising receiving lower and upper specification limits for at least one of the remaining article characteristics;
locating the specification limits associated with said at least one remaining article characteristic relative to the regression model between the predictor characteristic and said at least one remaining article characteristic.
10. The method of claim 9 further comprising determining the value of the predictor characteristic at which the upper prediction interval associated with the regression model between the predictor characteristic and said at least one remaining article characteristic intersects the upper specification limit for said at least one remaining article characteristic.
11. The method of claim 9 or 10 further comprising determining the value of the predictor characteristic at which the lower prediction interval associated with the regression model between the predictor characteristic and said at least one remaining article characteristic intersects the lower specification limit for said at least one remaining article characteristic.
12. The method of claim 6 further comprising receiving the lower and upper specification limits for the predictor characteristic;
and locating the upper and lower specification limits associated with the predictor characteristic.
13. The method of claim 8 further comprising receiving the lower and upper specification limits for the predictor characteristic;
and locating the upper and lower specification limits associated with the predictor characteristic.
14. The method of claim 3 further comprising receiving lower and upper specification limits for said at least one of the remaining article characteristics;
locating the lower and upper specification limits associated with said at least one of the remaining article characteristics;
receiving lower and upper specification limits for the predictor characteristic;
locating the upper specification limit associated with the predictor characteristic;
and determining a maximum article characteristic value for the predictor characteristic by selecting the lesser of (1) the upper specification limit for the predictor characteristic and (2) the value of the predictor characteristic at which the upper prediction interval intersects the upper specification limit for said at least one remaining article characteristic.
15. The method of claim 14 further comprising repeating the determining a maximum article characteristic value step for a desired number of remaining article characteristics in the plurality of article characteristics; and determining the most constraining maximum article characteristic value for the predictor characteristic by selecting the lowest maximum article characteristic value.
16. The method of claim 14 further comprising receiving lower and upper specification limits for at least one of the remaining article characteristics;
locating the lower specification limit associated with the predictor characteristic;
and determining a minimum article characteristic value for the predictor characteristic by selecting the greater of (1) the lower specification limit for the predictor characteristic and (2) the value of the predictor characteristic at which the lower prediction interval intersects the lower specification limit for said at least one remaining article characteristic.
17. The method of claim 16 further comprising determining an allowable range for the predictor characteristic subtracting the minimum article characteristic value from the maximum characteristic value.
18. The method of claim 16 further comprising repeating the determining a minimum article characteristic value step for a desired number remaining article characteristics in the plurality of article characteristics; and determining the most constraining minimum article characteristic value for the predictor characteristic by selecting the greatest minimum article characteristic value.
19. The method of claim 18 further comprising determining the maximum allowable range for the predictor characteristic by subtracting the most constraining minimum article characteristic value from the most constraining maximum characteristic value.
20. The method of claim 19 further comprising determining the target manufacturing value for the predictor characteristic by selecting a value between the most constraining minimum and maximum article characteristic values for the predictor characteristic.
21. The method of claim 19 further comprising determining the target manufacturing value for the predictor characteristic by selecting the midpoint value between the most constraining minimum and maximum values for the predictor characteristic.
22, The method of claim 21 further comprising receiving a target value for the predictor characteristic and a target value for at least one remaining article characteristic;
determining the intersection of the target value for the predictor characteristic and the target value of a first remaining article characteristic relative to the regression model between the predictor characteristic and the first remaining article characteristic.
23. The method of claim 1 wherein the selecting step comprises selecting the predictor characteristic based at least in part on an assessment of the capability of each article characteristic to be predictive of all or a subset of the article characteristics in the plurality of article characteristics.
24. The method of claim 23 wherein the selecting step comprises calculating the correlation coefficients between all or a subset of the article characteristics;
determining, based on the calculated correlation coefficients, a value indicating the predictive capability of a first article characteristic relative to all other article characteristics;
repeating the determining step for said all or a subset of the article characteristics;
and selecting a predictor characteristic based at least in part on the values indicating the predictive capabilities of the article characteristics.
25. The method of claim 24 wherein the predictor characteristic is selected as the article characteristic associated with the value indicating the highest predictive capability.
26. The method of claim 24 further comprising ranking the article characteristics based on the values computed in the determining step.
27. The method of claim 24 wherein the determining step comprises calculating the average correlation coefficient for each article characteristic.
28. The method of claim 24 wherein the determining step comprises calculating the average of the absolute values of the correlation coefficients for each article characteristic.
29. The method of claim 23 wherein the predictor characteristic is selected based on a graphical determination of the article characteristic having the greatest predictive capabilities.
30. The method of claim 23 wherein selection of the predictor characteristic is further based on factors associated with assessing each article characteristic.
31. The method of claim 30 wherein the factors comprise the economic factors associated with assessing each article characteristic.
32. The method of claim 30 wherein the factors comprise the technical factors associated with assessing each article characteristic.
33. The method of claim 28 further comprising ranking the article characteristics based on the values computed in the determining step; and wherein selection of the predictor characteristic is further based on economic or technical factors associated with assessing each article characteristic.
34. A method facilitating design and manufacturing processes, the method comprising receiving a plurality of article characteristic values associated with a set of articles having a range of variation as to a plurality of article characteristics;
determining the regression model(s) between a first article characteristic and at least one remaining article characteristic in the plurality of article characteristics;
receiving a target value for the first article characteristic and a target value for said at least one of the remaining article characteristic; and determining the intersection between the target value for the first article characteristic and a target value for said at least one remaining article characteristic.
35. The method of claim 34 wherein regression models are determined for all possible combinations of article characteristics in the plurality of article characteristics.
36. The method of claim 34 wherein regression models are determined for a subset of all possible combinations of article characteristics in the plurality of article characteristics.
37. The method of claim 34, 35 or 36 further comprising displaying the regression model(s) on a user interface display.
38. The method of claim 37 wherein the regression model(s) are graphically displayed in scatter diagrams on the user interface display.
39. The method of claim 34 further comprising receiving the lower and upper specification limits for said at least one remaining article characteristics;
locating the specification limits associated with said at least one remaining article characteristic.
40. The method of claim 39 further comprising receiving the lower and upper specification limits for the first article characteristic;
locating the lower and upper specification limits for the first article characteristic.
41. The method of claim 39 further comprising (a) determining the value of the first article characteristic at which the regression model intersects the upper specification limit for said at least one remaining article characteristic.
42. The method of claim 39 or 41 further comprising determining the value of the first article characteristic at which the regression model intersects the lower specification limit for said at least one remaining article characteristic.
43. The method of claim 41 further comprising repeating the determining step (a) for a desired number of remaining article characteristics; and determining the most constraining maximum value for the first article characteristic by selecting the lowest value of the first article characteristic associated with the determining step (a).
44. The method of claim 43 further comprising (b) determining the value of the first article characteristic at which the regression model intersects the lower specification limit for said at least one remaining article characteristic;
repeating the determining step for a desired number of remaining article characteristics; and determining the most constraining minimum value for the first article characteristic by selecting the greatest value of the first article characteristic associated with the determining step (b).
45. The method of claim 44 further comprising determining the target manufacturing value for the first characteristic by selecting the midpoint between the most constraining minimum and maximum values for the first article characteristic.
46. The method of 44 further comprising determining the maximum allowable range for the first article characteristic by subtracting the most constraining minimum value for the first article characteristic from the most constraining maximum value for the first article characteristic.
47. The method of claim 44 further comprising determining the target manufacturing value for the first characteristic by selecting a value between the most constraining minimum and maximum values for the first article characteristic.
48. The method of claim 41 further comprising receiving the lower and upper specification limits for the first article characteristic;
and locating the lower and upper specification limits associated with the first article characteristic;
repeating the determining step (a) for a desired number of remaining article characteristics; and determining the most constraining maximum value for the first article characteristic by selecting the lower of (l) the upper specification limit for the first article characteristic and (2) the lowest value computed in the determining step (a).
49. The method of claim 47 further comprising (b) determining the value of the first article characteristic at which the regression model intersects the lower specification limit for said at least one remaining article characteristic;
repeating the determining step (b) for a desired number of remaining article characteristics; and determining the most constraining minimum value for the first article characteristic by selecting the greater of (1) the lower specification limit for the first article characteristic and (2) the greatest value of the first article characteristic computed in the determining step (b).
50. A method facilitating design and manufacturing processes, the method comprising receiving a plurality of article characteristic values associated with a set of articles having a range of variation as to a plurality of article characteristics;
determining a first regression model between a first article characteristic and a second article characteristic;
determining at least a second regression model between the first article characteristic and at least one of the remaining article characteristics; and, facilitating a comparison between the regression models.
51. The method of claim 50 wherein regression models are determined for all possible combinations of article characteristics in the plurality of article characteristics.
52. The method of claim 50 wherein regression models are determined for a subset of all possible combinations of article characteristics in the plurality of article characteristics.
53. The method of claim 50, 51, or 52 further comprising displaying the regression model(s) on a user interface display.
54. The method of claim 53 wherein the regression models are graphically displayed in scatter diagrams on the user interface display.
55. The method of claim 50 further comprising receiving a target value as to at least two article characteristics;
as to a first article characteristic and a second article characteristic, locating the intersection of the target values of the first and second article characteristics relative to the regression model associated with the first and second article characteristics.
56. The method of claim 55 further comprising As to the first article characteristic and a third article characteristic, locating the intersection of the target values of the first and third article characteristics relative to the regression model associated with the first and third article characteristics.
57. The method of claim 50 further comprising receiving the lower and upper specification limits for the second article characteristic and a third article characteristic;
locating the specification limits associated with the second article characteristic relative to the regression model between the first article characteristic and the second article characteristic;
locating the specification limits associated with the third article characteristic relative to the regression model between the third article characteristic and the first article characteristic.
58. The method of claim 56 further comprising receiving the lower and upper specification limits for the first article characteristic;
locating the specification limits for the first article characteristic relative to the regression model between the first article characteristic and the second article characteristic; and locating the specification limits for the first article characteristic relative to the regression model between the first article characteristic and the third article characteristic.
59. A method facilitating design and manufacturing processes associated with the production of an article, the article having a plurality of article characteristics, at least two of the article characteristics having a target value and upper and lower specification limits, the method comprising generating a set of articles having a range of variation as to a plurality of article characteristics;
assessing the set of articles as to all or a subset of the plurality of article characteristics;
selecting a predictor characteristic from the plurality of article characteristics; and, determining the regression model(s) between the predictor characteristic and at least one of the remaining article characteristics in the plurality of article characteristics.
60. The method of claim 59 further comprising determining the intersection of the target value for the predictor characteristic and the target value of at least one remaining article characteristic relative to the regression model between the predictor characteristic and said at least one remaining article characteristic.
61. The method of claim 59 further comprising determining the respective upper and lower prediction intervals associated with the regression model between the predictor characteristic and said at least one of the remaining article characteristics.
62. The method of claim 60 further comprising determining the respective upper and lower prediction intervals associated with the regression model(s) between the predictor characteristic and said at least one of the remaining article characteristics.
63. The method of claim of 62 further comprising locating the lower and upper specification limits associated with said at least one remaining article characteristic;
locating the upper and lower specification limits associated with the predictor characteristic.
64. The method of claim 59 further comprising locating the specification limits associated with said at least one remaining article characteristic.
65. The method of claim 64 further comprising determining the value of the predictor characteristic at which the regression model intersects the upper specification limit for said at least one remaining article characteristic.
66. The method of claim 64 or 65 further comprising determining the value of the predictor characteristic at which the regression model intersects the lower specification limit for said at least one remaining article characteristic.
67. The method of claim 61 further comprising locating the specification limits associated with said at least one remaining article characteristic.
68. The method of claim 67 further comprising determining the value of the predictor characteristic at which the upper prediction interval associated with the regression model between the predictor characteristic and said at least one remaining article characteristic intersects the upper specification limit for said at least one remaining article characteristic.
69. The method of claim 67 or 68 further comprising determining the value of the predictor characteristic at which the lower prediction interval associated with the regression model between the predictor characteristic and said at least one remaining article characteristic intersects the lower specification limit for said at least one remaining article characteristic.
70. The method of claim 64 further comprising locating the upper and lower specification limits associated with the predictor characteristic.
71. The method of claim 66 further comprising locating the upper and lower specification limits associated with the predictor characteristic.
72. The method of claim 61 further comprising locating the lower and upper specification limits associated with said at least one remaining article characteristic.
locating the upper specification limit associated with the predictor characteristic;
and determining a maximum article characteristic value for the predictor characteristic by selecting the lesser of (1) the upper specification limit for the predictor characteristic and (2) the value of the predictor characteristic at which the upper prediction interval intersects the upper specification limit for said at least one remaining article characteristic.
73. The method of claim 72 further comprising repeating the determining a maximum article characteristic value step for a desired number of remaining article characteristics in the plurality of article characteristics; and determining the most constraining maximum article characteristic value for the predictor characteristic by selecting the lowest maximum article characteristic value.
74. The method of claim 72 further comprising locating the lower specification limit associated with the predictor characteristic;
and determining a minimum article characteristic value for the predictor characteristic by selecting the greater of (1) the lower specification limit for the predictor characteristic and (2) the value of the predictor characteristic at which the lower prediction interval intersects the lower specification limit for said at least one remaining article characteristic.
75. The method of claim 74 further comprising determining an allowable range for the predictor characteristic by subtracting the minimum article characteristic value from the maximum characteristic value.
76. The method of claim 74 further comprising repeating the determining a minimum article characteristic value step for a desired number of remaining article characteristics; and determining the most constraining minimum article characteristic value for the predictor characteristic by selecting the greatest minimum article characteristic value.
77. The method of claim 76 further comprising determining the maximum allowable range for the predictor characteristic by subtracting the most constraining minimum article characteristic value from the most constraining maximum characteristic value.
78. The method of claim 76 further comprising determining the target manufacturing value for the predictor characteristic by selecting a value between the most constraining minimum and maximum values for the predictor characteristic.
79. The method of claim 76 further comprising determining the target manufacturing value for the predictor characteristic by selecting the midpoint value between the most constraining minimum and maximum values for the predictor characteristic.
80. The method of claim 79 determining the intersection of the target value for the predictor characteristic and the target value of at least one remaining article characteristic relative to the regression model between the predictor characteristic and said at least one remaining article characteristic.
81. The method of claim 59 wherein the selecting step comprises selecting the predictor characteristic based at least in part on an assessment of the capabilities of each article characteristic to be predictive of the other article characteristics in the plurality of article characteristics.
82. The method of claim 81 wherein the selecting step comprises calculating the correlation coefficients between all or a subset of the article characteristics;
determining, based on the calculated correlation coefficients, a value indicating the predictive capability of a first article characteristic relative to all other article characteristics;
repeating the determining step for all article characteristics; and selecting a predictor characteristic based at least in part on the values indicating the predictive capabilities of the article characteristics.
83. The method of claim 82 wherein the predictor characteristic is selected as the article characteristic associated with the value indicating the highest predictive capability.
84. The method of claim 82 further comprising ranking the article characteristics based on the values computed in the determining step.
85. The method of claim 82 wherein the determining step comprises calculating the average correlation coefficient for each article characteristic.
86. The method of claim 82 wherein the determining step comprises calculating the average of the absolute values of the correlation coefficients for each article characteristic.
87. The method of claim 81 wherein the predictor characteristic is selected based on a graphical determination of the article characteristic having the greatest predictive capabilities.
88. The method of claim 81 wherein the selection of the predictor characteristic is further based on factors associated with assessing each article characteristic.
89. The method of claim 88 wherein the factors comprise the economic factors associated with assessing each article characteristic.
90. The method of claim 88 wherein the factors comprise the technical factors associated with assessing each article characteristic.
91. A method facilitating design and manufacturing processes, the method comprising generating a set of articles having a range of variation as to a plurality of article characteristics;
assessing the degree of correlation between the article characteristics; and, selecting a predictor characteristic from the plurality of article characteristics based on the assessing step.
92. The method of claim 91 further comprising determining a maximum allowable range for the predictor characteristic; and, subsequent to the determining step, verifying that subsequently generated articles comply with at least one design specification associated with said articles based on assessment of the predictor characteristic.
93. A method facilitating design, manufacturing, and other processes, the method comprising receiving a plurality of article characteristic values associated with a set of articles having a range of variation as to a plurality of article characteristics;
selecting a predictor characteristic from the plurality of article characteristics;
determining the regression model between the predictor characteristic and a first remaining article characteristic in the plurality of article characteristics, wherein the regression model includes lower and upper prediction boundaries receiving lower and upper specification limits for the predictor characteristic and the first remaining article characteristic;
locating, relative to the regression model between the predictor characteristic and the first remaining article characteristic, the compliance area bounded by the upper and lower specification limits associated with the first remaining article characteristic and the predictor characteristic;
locating the bounded regression area for the first remaining characteristic defined by the upper and lower prediction boundaries of the regression model and the upper and lower specification limits for the predictor characteristic; and identifying the relationship between the bounded regression area and the compliance area.
94. The method of claim 93 wherein the identified relationship characterizes the structure of the geometric relationship between the bounded regression area and the compliance area.
95. The method of claim 93 wherein the identified relationship characterizes the relationship between the perimeter elements that define the bounded regression area and the perimeter elements that define the compliance area.
96. The method of claim 93 wherein the identified relationship is one from the group consisting of a defect potential relationship, a robust relationship and a constraining relationship.
97. The method of claim 93 wherein the identifying step comprises determining whether the bounded regression area lies completely within the compliance area.
98. The method of claim 97 further comprising if the bounded regression area lies completely within the compliance area, setting the minimum and maximum predictor characteristic values associated with the first remaining article characteristic to the lower and upper specification limits, respectively, of the predictor characteristic.
99. The method of claim 93 wherein the identifying step comprises determining whether the bounded regression area extends above, below, or both above and below the compliance area over the specification limit range of the predictor characteristic; and if so, reporting a defect condition as to the first remaining article characteristic.
100. The method of claim 98 wherein the identifying step further comprises determining whether the bounded regression area extends above, below, or both above and below the compliance area over the specification limit range of the predictor characteristic; and if so, reporting a defect condition as to the first remaining article characteristic.
101. The method of claim 1 wherein the identifying step comprises determining whether any horizontal segment of the bounded regression area is contained completely within the compliance area and whether a second horizontal segment extends partially or completely outside of the compliance area; and if so, computing the minimum and maximum predictor characteristic values for the first remaining article characteristic.
102. The method of claim 101 wherein the computing step comprises determining the slope and intercept of the regression model between the predictor characteristic and the first remaining article characteristic;
determining the value of the predictor characteristic at which the upper prediction boundary corresponding to the regression model intersects the upper specification limit for the first remaining article characteristic;

determining the value of the predictor characteristic at which the lower prediction boundary corresponding to the regression model intersects the lower specification limit for the first remaining article characteristic;
if the slope of the regression model is positive, then:
setting the maximum predictor characteristic value associated with the first remaining article characteristic to the lesser of the upper specification limit of the predictor characteristic or the value of the predictor characteristic at which the upper prediction boundary corresponding to the regression model intersects the upper specification limit for the first remaining article characteristic; and setting the minimum predictor characteristic value associated with the first remaining article characteristic to the greater of the lower specification limit of the predictor characteristic or the value of the predictor characteristic at which the lower prediction boundary corresponding to the regression model intersects the lower specification limit for the first remaining article characteristic;
otherwise, if the slope of the regression model is negative, then setting the maximum predictor characteristic value associated with the first remaining article characteristic to the lesser of the upper specification limit of the predictor characteristic or the value of the predictor characteristic at which the lower prediction boundary corresponding to the regression model intersects the lower specification limit for the first remaining article characteristic; and setting the minimum predictor characteristic value associated with the first remaining article characteristic to the greater of the lower specification limit of the predictor characteristic or the value of the predictor characteristic at which the upper prediction boundary corresponding to the regression model intersects the upper specification limit for the first remaining article characteristic.
103. The method of claim 100 wherein the identifying step further comprises determining whether any horizontal segment of the bounded regression area is contained completely within the compliance area and whether a second horizontal segment extends partially or completely outside of the compliance area; and if so, computing the minimum and maximum predictor characteristic values for the first remaining article characteristic.
104. The method of claim 103 further comprising storing the resulting minimum and maximum predictor characteristic values in association with the corresponding remaining article characteristic in a data structure.
105. The method of claim 104 wherein the data structure is an array.
106. The method of claim 104 wherein the reporting a defect condition step comprises storing a defect identifier in association with the corresponding remaining article characteristic.
107. The method of claim 105 further comprising displaying the resulting minimum and maximum predictor characteristic values and/or defect identifiers in association with the corresponding remaining article characteristic.
108. The method of claim 93 wherein the identifying step comprises determining whether all vertical cross sections of the bounded regression area lie within the compliance area.
109. The method of claim 108 further comprising if all vertical cross sections of the bounded regression area lie within the compliance area, setting the minimum and maximum predictor characteristic values associated with the first remaining article characteristic to the lower and upper specification limits, respectively, of the predictor characteristic.
110. The method of claim 93 wherein the comparing step comprises determining whether all vertical cross-sections of the bounded regression area are fully or partially outside of the compliance area; and if so, reporting a defect condition as to the first remaining article characteristic.
111. The method of claim 93 wherein the comparing step comprises determining whether at least one vertical cross section of the bounded regression area is completely within the compliance region and whether at least one vertical cross section is partially or completely outside the compliance area; and if so, computing the minimum and maximum predictor characteristic values for the first remaining article characteristic.
112. The method of claim 111 wherein the computing step comprises determining the slope of the regression model between the predictor characteristic and the first remaining article characteristic;
determining the value of the predictor characteristic at which the upper prediction boundary corresponding to the regression model intersects the upper specification limit for the first remaining article characteristic;
determining the value of the predictor characteristic at which the lower prediction boundary corresponding to the regression model intersects the lower specification limit for the first remaining article characteristic;
if the slope of the regression model is positive, then:
setting the maximum predictor characteristic value associated with the first remaining article characteristic to the lesser of the upper specification limit of the predictor characteristic or the value of the predictor characteristic at which the upper prediction boundary corresponding to the regression model intersects the upper specification limit for the first remaining article characteristic; and setting the minimum predictor characteristic value associated with the first remaining article characteristic to the greater of the lower specification limit of the predictor characteristic or the value of the predictor characteristic at which the lower prediction boundary corresponding to the regression model intersects the lower specification limit for the first remaining article characteristic;
otherwise, if the slope of the regression model is negative, then setting the maximum predictor characteristic value associated with the first remaining article characteristic to the lesser of the upper specification limit of the predictor characteristic or the value of the predictor characteristic at which the lower prediction boundary corresponding to the regression model intersects the lower specification limit for the first remaining article characteristic; and setting the minimum predictor characteristic value associated with the first remaining article characteristic to the greater of the lower specification limit of the predictor characteristic or the value of the predictor characteristic at which the upper prediction boundary corresponding to the regression model intersects the upper specification limit for the first remaining article characteristic.
113. The method of claim 93 wherein the identifying step comprises determining whether the lower and upper boundaries of the bounded regression area are completely within the compliance region.
114. The method of claim 113 further comprising if the lower and upper boundaries of the bounded regression area are completely within the compliance region, setting the minimum and maximum predictor characteristic values associated with the first remaining article characteristic to the lower and upper specification limits, respectively, of the predictor characteristic.
115. The method of claim 93 wherein the identifying step comprises determining whether either of the lower and upper boundaries of the bounded regression area fail to intersect the compliance area; and if so, reporting a defect condition as to the first remaining article characteristic.
116. The method of claim 93 wherein the identifying step comprises determining whether the upper boundary of the bounded regression area intersects the upper boundary of the compliance area and the lower boundary of the bounded regression area intersects the compliance area; and, if so, computing the minimum and maximum predictor characteristic values for the first remaining article characteristic;
else, determining whether the lower boundary of the bounded regression area intersects the lower boundary of the compliance area and the upper boundary of the bounded regression area intersects the compliance area; and, if so, computing the minimum and maximum predictor characteristic values for the first remaining article characteristic.
117. The method of claim 24 wherein the computing step comprises determining the slope of the regression model between the predictor characteristic and the first remaining article characteristic;
determining the value of the predictor characteristic at which the upper prediction boundary corresponding to the regression model intersects the upper specification limit for the first remaining article characteristic;
determining the value of the predictor characteristic at which the lower prediction boundary corresponding to the regression model intersects the lower specification limit for the first remaining article characteristic;
if the slope of the regression model is positive, then:
setting the maximum predictor characteristic value associated with the first remaining article characteristic to the lesser of the upper specification limit of the predictor characteristic or the value of the predictor characteristic at which the upper prediction boundary corresponding to the regression model intersects the upper specification limit for the first remaining article characteristic; and setting the minimum predictor characteristic value associated with the first remaining article characteristic to the greater of the lower specification limit of the predictor characteristic or the value of the predictor characteristic at which the lower prediction boundary corresponding to the regression model intersects the lower specification limit for the first remaining article characteristic;
otherwise, if the slope of the regression model is negative, then setting the maximum predictor characteristic value associated with the first remaining article characteristic to the lesser of the upper specification limit of the predictor characteristic or the value of the predictor characteristic at which the lower prediction boundary corresponding to the regression model intersects the lower specification limit for the first remaining article characteristic; and setting the minimum predictor characteristic value associated with the first remaining article characteristic to the greater of the lower specification limit of the predictor characteristic or the value of the predictor characteristic at which the upper prediction boundary corresponding to the regression model intersects the upper specification limit for the first remaining article characteristic.
118. The method of claim 93 wherein the identifying step comprises computing the upper and lower prediction boundary values for the first remaining article characteristic at the upper and lower specification limits of the predictor characteristic;
determining whether the upper prediction boundary values in the computing step are both less than the upper specification limit for the first remaining article characteristic, and whether the lower prediction boundary values in the computing step are both greater than the lower specification limit for the first remaining article characteristic.
119. The method of claim 118 further comprising if the upper prediction boundary values in the computing step are both less than the upper specification limit for the first remaining article characteristic, and the lower prediction boundary values in the computing step are both greater than the lower specification limit for the first remaining article characteristic, then setting the minimum and maximum predictor characteristic values associated with the first remaining article characteristic to the lower and upper specification limits, respectively, of the predictor characteristic.
120. The method of claim 93 wherein the identifying step comprises computing the upper and lower prediction boundary values for the first remaining article characteristic at the upper and lower specification limits of the predictor characteristic;
if the upper prediction boundary values in the computing step are both greater than the upper specification limit for the first remaining article characteristic, then reporting a defect condition as to the first remaining article characteristic; and if the lower prediction boundary values in the computing step are both less than the lower specification limit for the first remaining article characteristic, then reporting a defect condition as to the first remaining article characteristic.
121. The method of claim 93 wherein the identifying step comprises computing the upper and lower prediction boundary values for the first remaining article characteristic at the upper and lower specification limits of the predictor characteristic;

determining whether one of the upper prediction boundary values in the computing step is less than, and the other of the upper prediction boundary values is greater than, the upper specification limit of the first remaining article characteristic, and both of the lower prediction boundary values are greater than the upper specification limit for the first remaining article characteristic; and if so, computing the minimum and maximum predictor characteristic values for the first remaining article characteristic;
else, determining whether one of the lower prediction boundary values in the computing step is less than, and the other of the lower prediction boundary values is greater than, the lower specification limit for the first remaining article characteristic, and whether the upper prediction boundary values in the computing step, are both less than the upper specification limit of the first remaining article characteristic; and, if so, computing the minimum and maximum predictor characteristic values for the first remaining article characteristic;
else, determining whether one of the upper prediction boundary values in the computing step is less than, and the other of the upper prediction boundary values is greater than, the upper specification limit of the first remaining article characteristic, and whether one of the lower prediction boundary values in the computing step is less than, and the other of the lower prediction boundary values is greater than, the lower specification limit for the first remaining article characteristic; and, if so, computing the minimum and maximum predictor characteristic values for the first remaining article characteristic.
122. The method of claim 121 wherein the computing step comprises determining the slope of the regression model between the predictor characteristic and the first remaining article characteristic;
determining the value of the predictor characteristic at which the upper prediction boundary corresponding to the regression model intersects the upper specification limit for the first remaining article characteristic;
determining the value of the predictor characteristic at which the lower prediction boundary corresponding to the regression model intersects the lower specification limit for the first remaining article characteristic;
if the slope of the regression model is positive, then:
setting the maximum predictor characteristic value associated with the first remaining article characteristic to the lesser of the upper specification limit of the predictor characteristic or the value of the predictor characteristic at which the upper prediction boundary corresponding to the regression model intersects the upper specification limit for the first remaining article characteristic; and setting the minimum predictor characteristic value associated with the first remaining article characteristic to the greater of the lower specification limit of the predictor characteristic or the value of the predictor characteristic at which the lower prediction boundary corresponding to the regression model intersects the lower specification limit for the first remaining article characteristic;
otherwise, if the slope of the regression model is negative, then setting the maximum predictor characteristic value associated with the first remaining article characteristic to the lesser of the upper specification limit of the predictor characteristic or the value of the predictor characteristic at which the lower prediction boundary corresponding to the regression model intersects the lower specification limit for the first remaining article characteristic; and setting the minimum predictor characteristic value associated with the first remaining article characteristic to the greater of the lower specification limit of the predictor characteristic or the value of the predictor characteristic at which the upper prediction boundary corresponding to the regression model intersects the upper specification limit for the first remaining article characteristic.
123. The method of claim 93 further comprising repeating the determining the regression model, receiving the specification limits, locating the compliance area, locating the bounded regression area, and identifying the relationship steps for all desired remaining article characteristics.
124. The method of claim 123 further comprising displaying the identified relationships.
125. The method of claim 123 further comprising storing the identified relationships in a data structure.
126. A method facilitating a determination of the magnitude and direction by which a pre-process characteristic would have to be adjusted to achieve a given design target, comprising receiving a plurality of article characteristic values associated with a set of articles having a range of variation as to a plurality of article characteristics;
selecting a predictor characteristic from the plurality of article characteristics;
determining the regression model between the predictor characteristic and a first remaining article characteristic in the plurality of article characteristics, receiving the target values for the predictor characteristic and the first remaining article characteristic;
computing, based on the regression model, the value of the first remaining article characteristic at the target value of the predictor characteristic;
determining the magnitude and direction of the offset for the first remaining article characteristic by computing the difference between the computed value of the first remaining article characteristic and the target value of the first remaining article characteristic;
storing the magnitude and direction of the offset in a data structure in association with an identifier for the first remaining article characteristic; and repeating the computing, determining and storing steps for all desired remaining characteristics.
127. The method of claim 126 further comprising displaying the resulting magnitudes and directions of the offsets in association with the corresponding remaining article characteristics.
128. A method facilitating analysis of the achievable gains in operating range associated with relaxing design tolerances corresponding to at least one article characteristic, comprising receiving a plurality of article characteristic values associated with a set of articles having a range of variation as to a plurality of article characteristics;
selecting a predictor characteristic from the plurality of article characteristics;
determining the regression model between the predictor characteristic and a first remaining article characteristic in the plurality of article characteristics, wherein the regression model includes lower and upper prediction boundaries;
receiving lower and upper specification limits for the predictor characteristic and the first remaining article characteristic;
76~

computing, based on the regression model, the minimum and maximum predictor characteristic values at which the first remaining article characteristic remains within the lower and upper specification limits of the first remaining article characteristic;
repeating the determining, receiving, and computing steps for all desired remaining article characteristics;
creating a most constraining minimum predictor characteristic list by ranking the remaining article characteristics by the respective minimum predictor characteristic values associated therewith; and starting with the remaining article characteristic associated with the greatest minimum predictor characteristic value:
computing the individual gain in operating range achieved by relaxing the applicable specification limit of the remaining article characteristic to the value corresponding to the minimum predictor characteristic value associated with the next remaining article characteristic in the ranked list;
computing the cumulative gain associated with relaxing the applicable specification limit of the corresponding article characteristic; and repeating the first and second computing steps for all desired remaining article characteristics.
129. The method of claim 128 further comprising creating a most constraining maximum predictor characteristic list by ranking the remaining article characteristics by the respective maximum predictor characteristic values associated therewith; and starting with the remaining article characteristic associated with the lowest maximum predictor characteristic value:
computing the individual gain in operating range achieved by relaxing the applicable specification limit of the remaining article characteristic to the value corresponding to the maximum predictor characteristic value associated with the next remaining article characteristic in the ranked list, computing the cumulative gain associated with relaxing the applicable specification limit of the corresponding article characteristic; and, repeating the first and second computing steps for all desired remaining article characteristics.
130. The method of claim 129 further comprising receiving a selection of at least one remaining article characteristic from either or both of the most constraining minimum or maximum predictor characteristic list;
if the selection includes a remaining article characteristic from the most constraining minimum predictor characteristic list, then:
setting the minimum predictor characteristic value to the minimum predictor characteristic value corresponding to the next article characteristic in the most constraining minimum predictor characteristic list, and for all article characteristics in the most constraining minimum predictor characteristic list up to the selected article characteristic, computing the new lower or upper specification limit for the article characteristic; and if the selection includes a remaining article characteristic from the most constraining maximum predictor characteristic list, then:
setting the maximum predictor characteristic value to the maximum predictor characteristic value corresponding to the next article characteristic in the most constraining maximum predictor characteristic list, and for all article characteristics in the most constraining maximum predictor characteristic list up to the selected article characteristic, determining the new lower or upper specification limit for the article characteristic.
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