# Patent

## Title
Systems and methods for presenting results of experiments

## Abstract

A method of automatically analyzing data from at least one data set including a plurality of process factors of interest and a process output of interest to determine the relationship between the factors of interest and the output of interest at a given significance level and preserving model hierarchy. The method includes the steps of calculating the effects of the factors of interest against the process output of interest, developing a model including the significant factors of interest and respective estimated coefficients and omitting the insignificant factors of interest, generating a representation of the model, and generating at least one graphical representation of the factors of interest.

## Background
FIELD OF THE INVENTION
The invention relates to systems and methods for assisting a user in designing experiments. Specifically, the invention provides a wizard for guiding a user through the design of experiments.
BACKGROUND OF THE INVENTION
Design of Experiments (DOE) is used to analyze a process to determine which process inputs have the greatest impact on the process. The process inputs, referred to as factors (e.g., temperature, quantity, etc.), have different levels. DOE allows a comparison of how different levels for the factors impact the process output or response. DOE uses randomization and replication to improve the results of the experiment. A concept called blocking allows variable factors to be removed from the experiment (e.g., differences between workers on a first shift and a second shift). Experiments are then created using full or fractional factorial designs.
SUMMARY OF THE INVENTION
In one embodiment, the invention provides a method of automatically analyzing data from at least one data set including a plurality of process factors of interest and a process output of interest to determine the relationship between the factors of interest and the output of interest at a given significance level and preserving model hierarchy. The method uses a computer to carry out the steps of calculating the effects of the factors of interest against the process output of interest, developing a model including the significant factors of interest and respective estimated coefficients and omitting the insignificant factors of interest, generating a representation of the model, and generating at least one graphical representation of the factors of interest. The graphical representation provides a first representation corresponding to factors of interest identified as significant and a second representation corresponding to factors of interest identified as insignificant. Calculating the effects includes calculating at least one of an analysis of variance test testing the significance of the individual effect of each factor of interest, coefficients and effect estimates for each factor of interest, and model comparison statistics, and identifying the factors of interest having significant effects relative to the given significance level and model hierarchy.
In another embodiment, the invention provides a method of automatically analyzing data from at least one data set including a plurality of process factors of interest and a process output of interest to determine the relationship between the factors of interest and the output of interest at a given significance level and preserving model hierarchy. The method uses a computer to carry out the steps of calculating the effects of the factors of interest against the process output of interest, and developing a model including the significant factors of interest and respective estimated coefficients and omitting the insignificant factors of interest. Calculating the effects includes calculating at least one of an analysis of variance test testing the significance of the individual effect of each factor of interest, coefficients and effect estimates for each factor of interest, and model comparison statistics, and identifying the factors of interest having significant effects relative to the given significance level and model hierarchy.
Other aspects of the invention will become apparent by consideration of the detailed description and accompanying drawings.



BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is a schematic diagram of a computer system for implementing a software program embodying the invention.
FIG. 2 is a spreadsheet for defining a design of experiments project.
FIGS. 3A and 3B are an embodiment of the operation of a wizard for designing experiments.
FIG. 4 is a user interface screen displayed by the wizard.
FIG. 5 is a process specific help screen displayed by the wizard.
FIG. 6 is a process specific help screen displayed by the wizard.
FIG. 7 is a process specific help screen displayed by the wizard.
FIG. 8 is a process specific help screen displayed by the wizard.
FIG. 9 is a process specific help screen displayed by the wizard.
FIG. 10 is a process specific help screen displayed by the wizard.
FIG. 11 is a process specific help screen displayed by the wizard.
FIG. 12 is a process specific help screen displayed by the wizard.
FIG. 13 is a user interface screen displayed by the wizard.
FIG. 14 is a user interface screen displayed by the wizard.
FIG. 15 is a user interface screen displayed by the wizard.
FIG. 16 is a user interface screen displayed by the wizard.
FIG. 17 is a user interface screen displayed by the wizard.
FIG. 18 is a user interface screen displayed by the wizard.
FIG. 19 is a user interface screen displayed by the wizard.
FIG. 20 is a user interface screen displayed by the wizard.
FIG. 21 is a user interface screen displayed by the wizard.
FIG. 22 is a user interface screen displayed by the wizard.
FIG. 23 is a user interface screen displayed by the wizard.
FIG. 24 is a user interface screen displayed by the wizard.
FIG. 25 is a user interface screen displayed by the wizard.
FIG. 26 is a user interface screen displayed by the wizard.
FIG. 27 is a design of experiments summary screen generated by the wizard.
FIG. 28 is a design of experiments response entry screen generated by the wizard.
FIG. 29 is a portion of analysis results spreadsheet generated by the software program.
FIG. 30 is a portion of analysis results spreadsheet generated by the software program.
FIG. 31 is a portion of analysis results spreadsheet generated by the software program.
FIG. 32 is a portion of analysis results spreadsheet generated by the software program.
FIG. 33 is a portion of analysis results spreadsheet generated by the software program.
FIG. 34 is a portion of analysis results spreadsheet generated by the software program.



DETAILED DESCRIPTION
Before any embodiments of the invention are explained in detail, it is to be understood that the invention is not limited in its application to the details of construction and the arrangement of components set forth in the following description or illustrated in the following drawings. The invention is capable of other embodiments and of being practiced or of being carried out in various ways.
FIG. 1 illustrates a system for performing DOE according to an embodiment of the present invention. The system includes a general purpose computer 100. The computer 100 provides a platform for operating a software program that guides a user through the design of experiments and then analyzes the results of the experiment. In the system identified, data and program files are input to the computer 100, which reads the files and executes the programs therein. Some of the elements of the computer 100 include a processor 105 having an input/output (IO) section 110, a central processing unit (CPU) 115, and a memory module 120. In one form, the software program for DOE is loaded into a non-transitory computer readable medium such as a memory 120 and/or a configured CD ROM (not shown) or other storage device (not shown). The software program includes instructions that are executed by the processor 105. The IO section 110 is connected to a keyboard 125 and an optional user input device or mouse 130. The keyboard 125 and mouse 130 enable the user to control the computer 100. IO section 110 is also connected to a monitor 135. In operation, computer 100 generates the user interfaces identified in FIGS. 4-34 and displays those user interfaces on the monitor 135. The computer also includes a CD ROM drive 140 and a data storage unit 145 connected to IO section 110. In some embodiments, the software program for DOE may reside on the storage unit 145 or in memory unit 120 rather than being accessed through the CD ROM drive using a CD ROM. Alternatively, CD ROM drive 140 may be replaced or supplemented by a floppy drive unit, a tape drive unit, a flash drive, or other data storage device. The computer 100 also includes a network interface 150 connected to IO section 110. The network interface 150 can be used to connect the computer 100 to a local area network (LAN), wide are network (WAN), internet based portal, or other network 155. Any suitable interface can suffice, including both wired and wireless interfaces. Thus, the software may be accessed and run locally as from CD ROM drive 140, data storage device 145, or memory 120, or may be remotely accessed through network interface 150. In the networked embodiment, the software may be stored remote from the computer 100 on a server or other appropriate hardware platform or storage device.
In one embodiment, the software is an add-in running in Microsoft® Excel®. A user loads the software onto the computer 100, and when the user starts up Excel® a menu selection for the add-in appears on a menu bar. By clicking through the menu selection and any submenus, the user is provided with a DOE menu. In some embodiments, the DOE menu provides the user with four choices: a DOE planning worksheet, a design wizard, a run default analysis, and a run custom analysis. Clicking the DOE planning worksheet opens a new worksheet 200 (FIG. 2). The worksheet 200 includes a plurality of cells for defining experiments. The worksheet 200, while optional, assists a user in planning experiments by having the user provide all the information that will be needed to design the experiments. In addition, spaces are provided for information that is useful for implementing the experiments (e.g., the process owner's name, the objective of the experiments, etc.).
Once the spreadsheet 200 has been completed, the user selects the design wizard function. FIGS. 3A and 3B show the operation of an embodiment of a DOE wizard. As shown in FIG. 4, the wizard provides a plurality of navigation buttons 405-430 and a progress bar 435 for each screen. Clicking an exit button 405 exits out of the wizard, deleting all previously entered data. Clicking a help button 410 opens a process specific help window with instructions for the particular portion of the DOE presently displayed by the wizard (FIGS. 5-12). Clicking a reset button 415 takes the user back to the start of the wizard, erasing all previously entered data. Clicking a back button 420 takes the user one screen back in the wizard. Clicking a next button 425 moves the user to the next screen. Clicking a finish button 430 causes the software to design the experiments based on the data entered into the wizard. The back button 420 is not available on a first screen 440. The next button 425 is only available when all necessary data has been entered for a particular screen of the wizard (the wizard provides default values in certain instances that do not need to be modified and some of the requested information is optional and need not be entered). The finish button 430 is only available when on the final screen of the wizard after all the necessary data has been entered. The progress bar 435 provides an indication of how far the user has progressed through the wizard.
The wizard provides two modes: (1) question and answer mode or (2) DOE map mode (see screen 440). The question and answer mode provides a high level of guidance to the user, asking questions for each step of design. The DOE map allows a user with more experience to select the type of experiments directly.
Referring back to FIG. 3A, if the user selects the question and answer mode (step 450), the wizard asks the user for the number of levels for each factor (step 455). The selections include only two levels for each factor or at least one factor having more than two levels (FIG. 13). If the user selects the DOE map mode (step 450), the user is presented with a map (FIG. 14) showing the available experiments and the criteria for each. The user selects a design of experiments from the map (step 460).
If the user selects the only two levels per factor option in the question and answer mode (step 455) or selects the full factorial, high resolution fractional factorial, or low resolution fractional factorial experiments in the DOE map mode (step 465), the wizard continues with requesting the user to enter the number of factors to be used in the experiments (step 470) (FIG. 15 for the question and answer mode and FIG. 16 for the DOE map mode). If the user selected five or more factors (step 472) the wizard prompts the user to select whether the experiments are for screening or testing ruggedness (step 473) (if the user selects four or less factors, this selection input is not provided). Screening is an economical experiment designed to examine a large number of possible factors to determine which of the factors might have the greatest effect on the outcome of the test (generally using high resolution fractional factorial design). Testing for ruggedness is an economical experiment designed to establish the ruggedness of a process to a large number of factors. This often involves the destructive testing of parts and typically only evaluates possible main effects (generally using low resolution fractional factorial design).
Next the user is presented with a screen having boxes for entering a name, a type, a unit type, a first level, and a second level for each of the factors chosen at step 470 (step 475) (FIG. 17A). The user is able to select the type of each factor as “categorical” or “numerical.” A categorical factor has a discrete number of values based on categories or groups. For example, a factor for location could be limited to east and west. A numerical factor has the possibility of a range of numeric values. For example, a factor for temperature theoretically has an infinite number of values within a range.
Next, the user is presented with a grid (FIG. 18). In the question and answer mode, the grid allows the user to select the number of runs to be executed for the experiments (step 480). This essentially selects the design of experiments from the full factorial, high resolution fractional factorial, or low resolution fractional factorial experiment designs. The grid allows the user to select the number of runs for the previously entered number of factors. For example, in FIG. 18, the user had selected five factors, and is able to choose runs of 8, 16, or 32 (highlighted in the rectangle). In the DOE map mode, the user previously selected the type of experiments. Therefore, only one selection is available in the grid. When the type of experiments is selected, a verification 482 of the type of experiments is shown below the grid (FIG. 19). In some embodiments, the wizard allows only a low resolution fractional factorial design when the user selects ruggedness testing. In some embodiments, the wizard only allows a high resolution fractional factorial design when the user selects screening.
Next, if available for the particular design chosen, the user is prompted to select whether to use blocks for the test or not (step 485) (FIG. 20). If the user elects to use blocks, the wizard prompts the user to enter the number of blocks to use, the blocking factor name, and the name of each block (step 490) (FIG. 21).
In the next screen (FIG. 22), the user is provided with data about the chosen experiments including the power 500. The wizard also shows how many replicates are required to raise the power to 80% 505 and 90% 510. The wizard prompts the user to enter the number of replicates the user desires (step 515). If at step 485, the user had selected not to enter blocks, the wizard moves directly to the replicates screen (FIG. 22) (step 520). If the user selects two or more replicates after having not selected blocks (step 525), the wizard asks whether the user wishes to run the replicates in blocks (step 530) (FIG. 23).
On the next screen (FIG. 24), the user is prompted to select the number of responses for the experiments and is then able to enter a name and type of units for each response (step 535). Finally, the user is prompted to enter a significance level (step 540). Once the significance level is selected, the finish button is highlighted and the user clicks on the finish button to design the experiments (step 545).
If in the question and answer mode at step 455 the user selected more than two issues or in the DOE map mode the user selected full factorial, the wizard prompts the user to enter the number of factors (step 550). If the user selects five or more factors (step 552) the wizard prompts the user to select whether the experiments are for screening or testing ruggedness (step 553) (if the user selects four or less factors, the selection input is not provided).
Next the wizard prompts the user for the number of levels for each factor (step 555), and the factor and level information (step 560) (FIG. 25). Where three or more levels are used, unlike the factor information for factors with only two levels, the wizard limits the type of factor to categorical. A confirmatory notification 562 indicates this to the user (see FIG. 17B).
Next, in FIG. 26, the wizard prompts the user for the number of replicates (step 565), and if the replicates are greater than one, allows the user to select blocking (step 570). The user is then prompted to select the number of responses for the experiments and is then able to enter a name and type of units for each response (step 575). Finally, the user is prompted to enter a significance level (step 540). Once the significance level is selected, the finish button is highlighted and the user clicks on the finish button to design the experiments (step 545).
FIGS. 27 and 28 are a sample of a design of experiments. The experiments have three factors, using full factorial experiments with one replication and one response. The experiments were run and response data entered into the table. Once all the experiments have been run, and the results entered into the table, the user selects a run default analysis option from a pull-down menu. The system runs the analysis and provides the results of the analysis in several forms shown in a response worksheet (FIGS. 29-34).
The results are given in an effect table 600, an ANOVA table 605, a recommended model 610, a half normal plot 615, a Pareto chart 620, a normal probability plot 625, a versus fits plot 630, a versus order plot 635, a histogram 640, a plurality of main effect plots 645-655, a plurality of interaction plots 660-665, and a cube plot 670. For the main effect plots 645-655, the interaction plots 660-665, and the cube plot 670, a pull-down menu 675 allows the user to determine which factor or interaction to show in each graph.
The software analyzes the data, and determines which factors and interactions are significant. The software then highlights the significant factors and interactions and produces a recommended model. For example, the half normal plot highlights (e.g., by color and symbol) the factors or interactions that are significant. In the example shown, factors A and B and interaction AB are significant and are shown as golden squares. The other factors and interactions are shown as blue diamonds. Each of the factors and interactions are also labeled in the chart. Thus a user can quickly identify the significant factors by simply viewing the plot.
Similarly, in the Pareto chart, the factors and interactions that are significant are grouped together and shown in gold, while the less significant factors and interactions are shown in blue.
A recommended model (in the example: Response 1=0.7*A+1.825*B+2.2*AB+13.825) is automatically generated by the software, providing a user who is not fluent in the analysis with an optimum model or saving a fluent user the time needed to generate the model.
Various features and advantages of the invention are set forth in the following claims.

## Claims

1. A method of automatically analyzing experimental data from at least one data set including a plurality of process factors of interest and a process output of interest to model the relationship between the factors of interest and the output of interest at a given significance level and preserving model hierarchy such that the model includes the factors of interest involved in a significant interaction, the method comprising:
calculating, using a computer, effects of the factors of interest on the process output of interest, including
performing an analysis of variance test to calculate a significance of the individual effect of each factor of interest and interactions between two or more of the factors of interest,
calculating coefficients and effect estimates for each factor of interest, and
calculating model comparison statistics,

comparing the significance calculated for each factor of interest and each interaction to the given significance level and identifying a factor of interest or an interaction as having a significant effect if the significance calculated for the factor of interest or the interaction satisfies the given significance level and identifying a factor of interest or an interaction as having an insignificant effect if the significance calculated for the factor of interest or the interaction does not satisfy the given significance level;
developing, using the computer, a recommended model including each factor of interest and interaction identified as having a significant effect and each factor of interest involved in an interaction identified as having a significant effect multiplied by the coefficient for the factor of interest and omitting each factor of interest and interaction identified as having an insignificant effect, the recommended model representing the relationship between significant factors of interest and the process output of interest;
generating a representation of the model; and
generating at least one graphical representation of the factors of interest, the graphical representation providing a first representation corresponding to the factors of interest and interactions identified as having a significant effect, including factors of interest involved in a significant interaction, and a second representation corresponding to the factors of interest and interactions identified as having an insignificant effect.

2. The method of claim 1, further comprising automatically determining the relationship between the factors of interest and a second output of interest at a given significance level and preserving model hierarchy.

3. The method of claim 1, wherein the at least one graphical representation of the factors of interest includes a half normal graph.

4. The method of claim 1, wherein the at least one graphical representation of the factors of interest includes a Pareto chart.

5. The method of claim 1, further comprising displaying, at least one graphical representation of the factors of interest, the factors of interest identified as having a significant effect in a first color and displaying the factors of interest identified as having an insignificant effect in a second color, the first color different from the second color.

6. The method of claim 1, further comprising displaying, at least one graphical representation of the factors of interest, the factors of interest identified as having a significant effect in a first shape and displaying the factors of interest identified as having an insignificant effect in a second shape, the first shape different from the second shape.

7. The method of claim 1, further comprising displaying, at least one graphical representation of the factors of interest, the factors of interest identified as having a significant effect in a first color and a first shape and displaying the factors of interest identified as having an insignificant effect in a second color and a second shape, the first color different from the second color and the first shape different from the second shape.

8. The method of claim 1, further comprising grouping the factors of interest identified as having a significant effect together on the at least one graphical representation of the factors of interest.

9. The method of claim 1, wherein the method is performed by an add-in of spreadsheet program.

10. The method of claim 1, wherein the model and the at least one graphical representation of the factors of interest are displayed on a spreadsheet.

11. Non-transitory computer-readable medium encoded with a plurality of processor-executable instructions for automatically analyzing experimental data from at least one data set including a plurality of process factors of interest and a process output of interest to model the relationship between the factors of interest and the output of interest at a given significance level and preserving model hierarchy such that the model includes the factors of interest involved in a significant interaction, the instructions comprising:
calculating effects of the factors of interest on the process output of interest, including
performing an analysis of variance test to calculate a significance of the individual effect of each factor of interest and interactions between two or more of the factors of interest,
calculating coefficients and effect estimates for each factor of interest, and
calculating model comparison statistics;

comparing the significance calculated for each factor of interest and each interaction to the given significance level and identify a factor of interest or an interaction as having a significant effect if the significance calculated for the factor of interest or the interaction satisfies the given significance level and identify a factor of interest or an interaction as having an insignificant effect if the significance calculated for the factor of interest or the interaction does not satisfy the given significance level;
developing a recommended model including each factor of interest and interaction identified as having a significant effect and each factor of interest involved in an interaction identified as having a significant effect multiplied by the coefficient for the factor of interest and omitting each factor of interest and interaction identified as having an insignificant effect, the recommended model representing the relationship between significant factors of interest and the process output of interest;
generating a representation of the model; and
generating at least one graphical representation of the factors of interest, the graphical representation providing a first representation corresponding to the factors of interest and interactions identified as having a significant effect, including factors of interest involved in a significant interaction, and a second representation corresponding to the factors of interest and interactions identified as having an insignificant effect.

12. The computer-readable medium of claim 11, further comprising instructions for automatically determining the relationship between the factors of interest and a second output of interest at a given significance level and preserving model hierarchy.

13. The computer-readable medium of claim 12, further comprising instructions for developing a second model for the second output of interest including the significant factors of interest and respective estimated coefficients and omitting the insignificant factors of interest.

14. The computer-readable medium of claim 12, further comprising instructions for displaying the model in a first worksheet and displaying the second model in a second worksheet.