The response is coffee Strength. It is measured as total dissolved solids, using a refractometer. The coffee is brewed using a single cup coffee dripper and measured five minutes after the liquid is released from the grounds.
Four factors are identified for the study: Grind, Temperature, Time, and Charge. Coffee is brewed at three stations in the work area. To account for variation due to brewing location, Station is included in the study as a blocking factor. The following describes the factors:
Grind is the coarseness of the grind. Grind is set at two levels, Medium and Coarse.
Temperature is the temperature in degrees Fahrenheit of the water measured immediately before pouring it over the grounds. Temperature is set at 195 and 205 degrees Fahrenheit.
Time is the brewing time in minutes. Time is set at 3 or 4 minutes.
Charge is the amount of coffee placed in the cone filter, measured in grams of coffee beans per ounce of water. Charge is set at 1.6 and 2.4.
Station is the location where the coffee is brewed. The three stations are labeled as 1, 2, and 3.
Factors and Range of Settings for Coffee Experiment summarizes information about the factors and their settings. The factors and levels are also given in the Coffee Factors.jmp sample data table, located in the Design Experiment folder.
Grind is categorical with two levels.
Temperature, Time, and Charge are continuous.
Station is a blocking factor with three levels.
The apparatus used in running the coffee experiment is shown in Coffee Experiment Apparatus. This is the setup at one of the three brewing stations. The two other stations have the same type of equipment.
Coffee Experiment Apparatus
1.
Select DOE > Custom Design.
2.
Double-click Y under Response Name and type Strength.
Note that the default Goal is Maximize. Your goal is to find factor settings that enable you to brew coffee with a target strength of 1.3, within limits of 1.2 and 1.4.
3.
Click on the default Goal of Maximize and change it to Match Target.
Selection of Match Target as the Goal
4.
Click under Lower Limit and type 1.2.
5.
Click under Upper Limit and type 1.4.
6.
Leave the area under Importance blank.
1.
Click Add Factor > Categorical > 2 Level.
2.
Type Grind over the default Name of X1.
4.
Type 3 next to Add N Factors. Then click Add Factor > Continuous.
Temperature (195 and 205)
Time (3 and 4)
Charge (1.6 and 2.4)
6.
Click Add Factor > Blocking > 4 runs per block.
7.
Type Station over the default Name of X5.
Completed Responses and Factors Outlines
8.
Click Continue.
2.
Select Help > Sample Data Library and open Design Experiment/Coffee Factors.jmp.
Design Generation Outline shows the Model outline. The Model outline is where you specify your assumed model, which contains the effects that you want to estimate. See Specify. The list that appears by default shows all main effects as Necessary, indicating that the design is capable of estimating all main effects. Because your main interest at this point is in the main effects of the factors, you do not add any effects to the Model outline.
Model Outline with Main Effects Only
Because the Custom Design algorithm begins with a random starting design, your design might differ from the one shown in Design for Coffee Experiment. To obtain a design with exactly the same runs and run order, perform the following steps before generating your design:
3.
6.
Design Generation Outline
1.
Click Make Design.
The Design outline shows the design (Design for Coffee Experiment). If you did not follow the steps in Steps to Duplicate Results (Optional), your design might be different from the one in Design for Coffee Experiment. This is because the algorithm begins with a random starting design.
Design for Coffee Experiment
Specify the order of runs in your data table using the Output Options panel. The default selection, Randomize within Blocks, is appropriate. This selection arranges the runs in a random order for each Station.
Output Options
1.
Click Make Table.
The data table shown in Custom Design Table opens. Keep in mind that, if you did not follow the steps in Steps to Duplicate Results (Optional), your design table might be different. Your design table represents another optimal design.
Custom Design Table
At this point, you perform the experiment. At each Station, four runs are conducted in the order shown in the design table. Equipment and material are reset between runs. For example, if two consecutive runs require water at 195 degrees, separate 12-ounce batches of water are heated to 195 degrees after the heating container cools. The Strength measurements are recorded.
Your design and the experimental results for Strength are given in the Coffee Data.jmp sample data table (Coffee Design with Strength Results), located in the Design Experiment folder.
Coffee Design with Strength Results
The Custom Design platform facilitates the task of data analysis by saving a Model script to the design table that it creates. See Custom Design Table. Run this script after you conduct your experiment and enter your data. The script opens a Fit Model window containing the effects that you specified in the Model outline of the Custom Design window.
1.
Select Help > Sample Data Library and open Design Experiment/Coffee Data.jmp.
Model Specification Window
3.
Select the Keep dialog open option.
4.
Click Run.
Effect Summary and Actual by Predicted Plot for Full Model
The model is significant, as indicated by the Actual by Predicted Plot. The notation P = 0.0041, shown below the plot, gives the significance level of the overall model test.
The Effect Summary report shows that Charge, Station, and Time are significant at the 0.05 level.
The Effect Summary report also shows that Temperature and Grind are not significant.
Because Temperature and Grind appear not to be active, they contribute random noise to the model. Refit the model without these effects to obtain more precise estimates of the model parameters associated with the active effects.
1.
In the Model Specification window, select Temperature and Grind in the Construct Model Effects list.
2.
Click Remove.
3.
Change the Emphasis to Effect Screening.
4.
Click Run.
Partial Results for Reduced Model
Prediction Profiler
The first two plots in the top row of the graph show how Strength varies for one of the factors, given the setting of the other factor. For example, when Charge is 2, the line in the plot for Time shows how predicted Strength changes with Time.
The values to the left of the top row of plots give the Predicted Strength (in red) and a confidence interval for the mean Strength for the selected factor settings.
The right-most plot in the top row shows the desirability function for Strength. The desirability function indicates that the target of 1.3 is most desirable. Desirability decreases as you move away from that target. Desirability is close to 0 at the limits of 1.2 and 1.4.
Explore various factor settings by dragging the red dashed vertical lines in the columns for Time and Charge. Since there are no interactions in the model, the profiler indicates that increasing Charge increases Strength. Also, Strength seems to be more sensitive to changes in Charge than to changes in Time.
Since Station is a blocking factor, it does not appear in the Prediction Profiler. However, you might like to see how predicted Strength varies by Station. To include Station in the Prediction Profiler, follow these steps:
A Factor Settings window appears with columns for Time, Charge, and Station. Under Station, notice that the box corresponding to Show is not selected. This indicates that Station is not shown in the Prediction Profiler.
2.
Select the box under Station in the row corresponding to Show.
3.
Deselect the box under Station in the row corresponding to Lock Factor Setting.
Factor Settings Window
4.
Plots for Station appear in the Prediction Profiler.
5.
Click in either plot above Station to insert a dashed red vertical line.
Prediction Profiler Showing Results for Station 1
Prediction Profiler Showing Results for Station 3
The predicted Strength in the center of the design region for Station 1 is 1.44. For Station 3, the predicted Strength is about 1.18. The magnitude of the difference indicates that you need to address Station variability. Better control of Station variation should lead to more consistent Strength. Once Station consistency is achieved, you can determine common optimal settings for Time and Charge.