In contrast to a split-split-plot design, the second-stage factors are not nested within the first-stage factors. After the first stage, the batches are subdivided and formed into new batches. Therefore, both the first- and second-stage factors are applied to whole batches.
Although factors at both stages might be equally hard-to-change, in order to distinguish these factors, JMP denotes the first stage factors as very-hard-to-change and the second-stage factors as hard-to-change. Additional factors applied to experimental units after the second processing stage are considered easy-to-change.
This example is based on an experiment to improve the open circuit voltage (OCV) in battery cells (Vivacqua and Bisgaard, 2004). You need to minimize the OCV in order to keep the cells from discharging on their own.
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Four factors (A1, A2, A3, and A4) are applied to the assembly process. You can run 16 trials for the first-stage factors.
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Two factors (C5 and C6) are applied to the curing process. Because curing requires a 5-day cycle time, you can run only 6 cycles (30 days) for the second-stage factors. Using six curing cycles gives you partial replication of the curing settings, enabling you to test for curing effects.
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The experiment has 48 experimental units. Note that the first- and second-stage factors are crossed.
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1.
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Select DOE > Custom Design.
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2.
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a.
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Select Load Factors from the Custom Design red triangle menu.
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b.
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Open the Battery Factors.jmp sample data table, located in the Design Experiment folder.
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c.
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5.
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Type 6 next to Add N Factors.
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6.
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Click Add Factor > Continuous.
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Figure 4.76 Responses and Factors Outlines
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10.
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Click Continue.
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11.
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Select Interactions> 2nd in the Model outline.
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12.
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In the Design Generation outline, select the option Hard to change factors can vary independently of Very Hard to change factors.
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See Figure 4.77. Checking this option creates a two-way split-plot design. If this option is not checked, the design is treated as a split-split-plot design, with nesting of factors at the two levels.
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13.
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Type 16 as the Number of Whole Plots.
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Type 6 as the Number of Subplots.
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Under Number of Runs, type 48 next to User Specified.
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Figure 4.77 Design Generation Outline
Note: Setting the Random Seed in step 16 and Number of Starts in step 17 reproduces the exact results shown in this example. In constructing a design on your own, these steps are not necessary.
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16.
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(Optional) From the Custom Design red triangle menu, select Set Random Seed, type 1866762673, and click OK.
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(Optional) From the Custom Design red triangle menu, select Number of Starts, type 21, and click OK.
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18.
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Click Make Design.
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19.
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Click Make Table.
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Figure 4.78 Partial View of Design Table
The design table shows 16 levels for Whole Plots. For each level of Whole Plots, the settings of the four assembly factors are constant. From each level of Whole Plots, three batches of 500 batteries (Subplots) are randomly assigned to settings of the curing factors. Two sets of curing conditions are replicated (C1 = -1, C2 = 1 and C1 = 1, C2 = 1). To see this, select columns C1 and C2, right-click in the header area, and select Sort > Ascending.
The Battery Data.jmp sample data table contains experimental results for the design that you generated.
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In the Table panel, click the green triangle next to the Model script.
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The factor Whole Plots has the Attribute called Random Effects (&Random). This specifies that the levels of Whole Plots are random realizations. They have an associated error term.
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The analysis Method is REML (Recommended). This method is specified precisely because the model contains random effects. For more information about REML models, see Restricted Maximum Likelihood (REML) Method in the Fitting Linear Models book.
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Check the option to Keep dialog open.
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Click Run.
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Figure 4.79 Report for Full Model
The Parameter Estimates report indicates that four two-way interactions, A1*C1, A1*C2, A2*C1, and A4*C2, and two main effects, A1 and A4, are significant at the 0.05 level.
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In the Table panel of Battery Data.jmp, click the green triangle next to the Reduced Model 1 script.
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The script opens a Fit Model window where insignificant interactions have been removed. The remaining effects are all main effects and the four two-way interactions A1*C1, A1*C2, A2*C1, and A4*C2. You are reducing the model in a conservative fashion.
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Click Run.
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Figure 4.80 Report for Preliminary Reduced Model
Notice that the main effect C2 is now significant at the 0.05 level (Prob>|t| = 0.0331)
The main effect A3 is the only main effect that is not significant and not involved in a two-way interaction.
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Click Run.
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Figure 4.81 Report for Reduced Model
The REML Variance Component Estimates report shows that the variance component associated with Whole Plots is about six times as large as the variance component for Subplots. This suggests that the assembly process is more variable than the curing process. Also, the within (Residual) error is larger than that for Subplots. Efforts to reduce variation should focus on the assembly process and on battery-to-battery differences.
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From the red triangle next to Response OCV, select Factor Profiling > Profiler.
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From the red triangle next to Prediction Profiler, select Optimization and Desirability > Maximize Desirability.
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