Example: pouch-seal strength
22 independent sealing runs: eight two-level combinations repeated on each of two days, plus three center runs per day. A block is one experimental day; keep its column assigned so the model accounts for day differences.
Download the recorded measurements (CSV)This is the same recorded example used in Help. The CSV contains factor settings and measured responses to import together. Use Open example in a practice copy in Help to prefill the settings.
1. Create the workspace
In the sidebar, open Design of Experiments and create an analysis. Name it, select New blank worksheet, then choose Create analysis.
2. Import the measurements
Download the example CSV above and import it into the worksheet. Choose Comma as the delimiter, Dot as the decimal separator and First row contains column names. Keep each row’s response, factor settings, point type and execution order together.
3. Choose the study and enter factors
On Inputs, choose Analyze existing worksheet for Task and Full factorial for Design family.
Under Factors, use Add factor or remove a row until there are 3 factors. Keep this order and set Type to Numeric for each factor.
Enter the Factor name, Unit, Low and High values below.
| Factor | Factor name | Unit | Low | High |
|---|---|---|---|---|
| A | jaw_temperature_c | °C | 150 | 170 |
| B | dwell_time_s | s | 0.8 | 1.2 |
| C | jaw_pressure_mpa | MPa | 0.25 | 0.35 |
Leave Numeric levels, optional blank.
4. Assign the input columns
Under Response mappings, open each column picker and select the matching worksheet column.
| Worksheet column | Input field |
|---|---|
jaw_temperature_c | Factor jaw_temperature_c |
dwell_time_s | Factor dwell_time_s |
jaw_pressure_mpa | Factor jaw_pressure_mpa |
Assign seal_strength_n_per_15mm to Response 1 and enter 1 in Number of responses. Assign run_order to Execution order and point_type to Center point indicator. For Center point column convention, choose Point type (center / factorial / fractional / star / axial / edge / edge_midpoint).
Assign block to Block to keep the two experimental days in the model.
5. Set the model and plots
Under Model, choose Default hierarchical model for Model terms and enter 95 in Confidence level (%). Check Include center-point adjustment in model. Leave Calculate predictions unchecked.
Open Plot options. Check Effect estimates and Residual diagnostics. Leave Response contours unchecked. Leave Pareto view, Effect probability plot, Interaction plot and 3D surface unchecked.
6. Analyze worksheet
Choose Analyze worksheet, then open Results. This fits the recorded measurements; it does not generate or randomize a new run plan.
7. Interpret results
Start with the recorded runs
All 22 sealing runs are included. The eight low/high combinations were repeated on each of two days, with three center runs per day. The model adjusts for the two days. Each response is the measured strength of an independently produced seal.
Check whether the model misses a pattern
Look at Lack of Fit in Adjusted term ANOVA. Its p-value is 0.9725, so this test does not detect a missing pattern at the 5% level. This does not prove the model is correct. The day effect has p = 0.01595; keep the block adjustment when comparing settings.
Read the effects
Temperature has the largest fitted high-minus-low effect: about +5.97 N per 15 mm. Dwell adds about +3.99 and pressure +1.25. Temperature × dwell is about +2.65; temperature × pressure is about −1.51. An interaction means the effect of one factor changes with another setting. These main effects do not apply unchanged to every combination.
Fitted high-minus-low effects with 95% confidence intervals. View full-size chart (opens in a new tab) Read a residual
A residual is the measured response minus the fitted value. Run 11 measured 23.87 N per 15 mm; the model fitted 22.55, leaving about +1.32 unexplained. This is the largest absolute raw residual. On the plot, look for curves, changing spread or unusual points.
Residuals in N per 15 mm against the fitted response. View full-size chart (opens in a new tab) Check the run sequence
The horizontal axis follows recorded execution order. Look for drift, cycles or a sudden change in the residuals. A pattern can suggest that the model missed a change during the experiment; the plot does not identify its cause.
Residuals in N per 15 mm in recorded execution order. View full-size chart (opens in a new tab) Choose a confirmation run
Review the records for unusual runs and compare combinations with their interactions and day adjustment. Confirm a promising, feasible setting with fresh independent seals. The largest main effect alone does not establish the best operating recipe.
More details: read each result section
Complete result tables use six significant digits, as in Help.
Model overview
Analyzed runs is 22; Missing runs is 0. DF counts the information available for the model and residual error. S is the residual standard deviation in N per 15 mm. R² describes variation fitted in these runs; adjusted R² accounts for model size. See Prediction and coefficient detail for PRESS and predicted R². A high R² does not establish model adequacy. Read the lack-of-fit test and residual plots.
| Statistic | Value |
|---|---|
| Response | seal_strength_n_per_15mm |
| Analyzed runs | 22 |
| Missing responses | 0 |
| Model rank | 9 |
| Residual degrees of freedom | 13 |
| S | 0.565919 |
| R² | 0.983747 |
| Adjusted R² | 0.973744 |
| PRESS | 9.07951 |
| Predicted R² | 0.964555 |
| Confidence level | 0.95 |
| Lack of fit available | Yes |
Adjusted term ANOVA
Source names the model term or error component. Type distinguishes adjusted term tests from totals and error decomposition. DF is degrees of freedom; SS is sum of squares; MS is SS divided by DF. F compares variation with its error estimate; p-value measures evidence against the tested null assumption. Read Lack of Fit before relying on individual effects. A dash means a statistic is not applicable.
| Source | Type | DF | SS | MS | F | p-value |
|---|---|---|---|---|---|---|
| jaw_temperature_c | adjusted | 1 | 142.325 | 142.325 | 444.398 | 1.95327e-11 |
| dwell_time_s | adjusted | 1 | 63.6006 | 63.6006 | 198.588 | 2.97481e-9 |
| jaw_pressure_mpa | adjusted | 1 | 6.2001 | 6.2001 | 19.3593 | 0.000717766 |
| jaw_temperature_c × dwell_time_s | adjusted | 1 | 28.037 | 28.037 | 87.5433 | 3.87092e-7 |
| jaw_temperature_c × jaw_pressure_mpa | adjusted | 1 | 9.1204 | 9.1204 | 28.4777 | 0.000135106 |
| dwell_time_s × jaw_pressure_mpa | adjusted | 1 | 0.245025 | 0.245025 | 0.76507 | 0.397618 |
| Block | adjusted | 1 | 2.45557 | 2.45557 | 7.66731 | 0.0159483 |
| Center point | adjusted | 1 | 0.00950303 | 0.00950303 | 0.0296724 | 0.865888 |
| Model | summary | 8 | 251.993 | 31.4991 | 98.3535 | 2.27367e-10 |
| Error | summary | 13 | 4.16344 | 0.320265 | — | — |
| Total | summary | 21 | 256.157 | 12.1979 | — | — |
| Pure Error | decomposition | 4 | 2.78713 | 0.696783 | — | — |
| Lack of Fit | decomposition | 9 | 1.37631 | 0.152923 | 0.21947 | 0.972452 |
Coefficients
Term names a coded model term. Estimate is its fitted coefficient; SE measures uncertainty; t and p-value test a zero coefficient. CI low and CI high bound its 95% interval. Numeric low, midpoint and high settings are coded −1, 0 and +1. With interactions or squares, a main coefficient does not describe the change at every setting.
| Term | Estimate | SE | t | p-value | CI low | CI high |
|---|---|---|---|---|---|---|
| Intercept | 22.935 | 0.14148 | 162.108 | 7.05502e-23 | 22.6294 | 23.2406 |
| jaw_temperature_c | 2.9825 | 0.14148 | 21.0807 | 1.95327e-11 | 2.67685 | 3.28815 |
| dwell_time_s | 1.99375 | 0.14148 | 14.0921 | 2.97481e-9 | 1.6881 | 2.2994 |
| jaw_pressure_mpa | 0.6225 | 0.14148 | 4.39992 | 0.000717766 | 0.316851 | 0.928149 |
| jaw_temperature_c × dwell_time_s | 1.32375 | 0.14148 | 9.35646 | 3.87092e-7 | 1.0181 | 1.6294 |
| jaw_temperature_c × jaw_pressure_mpa | -0.755 | 0.14148 | -5.33645 | 0.000135106 | -1.06065 | -0.449351 |
| dwell_time_s × jaw_pressure_mpa | 0.12375 | 0.14148 | 0.874683 | 0.397618 | -0.181899 | 0.429399 |
| Block · contrast 1 | -0.334091 | 0.120654 | -2.76899 | 0.0159483 | -0.594749 | -0.0734329 |
| Center point | -0.0466667 | 0.270913 | -0.172257 | 0.865888 | -0.631939 | 0.538606 |
Factorial effects
Effect is the fitted high-minus-low contrast. SE measures uncertainty, and CI low and CI high give its 95% interval. Standardized effect is the absolute effect divided by its SE. An interaction means a factor’s effect changes with another setting.
| Term | Effect | SE | CI low | CI high | Standardized effect |
|---|---|---|---|---|---|
| jaw_temperature_c | 5.965 | 0.28296 | 5.3537 | 6.5763 | 21.0807 |
| dwell_time_s | 3.9875 | 0.28296 | 3.3762 | 4.5988 | 14.0921 |
| jaw_pressure_mpa | 1.245 | 0.28296 | 0.633703 | 1.8563 | 4.39992 |
| jaw_temperature_c × dwell_time_s | 2.6475 | 0.28296 | 2.0362 | 3.2588 | 9.35646 |
| jaw_temperature_c × jaw_pressure_mpa | -1.51 | 0.28296 | -2.1213 | -0.898703 | 5.33645 |
| dwell_time_s × jaw_pressure_mpa | 0.2475 | 0.28296 | -0.363797 | 0.858797 | 0.874683 |
Row diagnostics
Row ID identifies the worksheet row; Run order locates it in the experiment sequence. Status states whether it was analyzed. Observed is the measurement; Fit is the model value; Residual is Observed minus Fit. Standardized residual adjusts for residual variation and leverage. Leverage measures how unusual the model inputs are. All recorded rows are shown. Investigate an unusual row before changing or excluding it.
| Row ID | Run order | Status | Observed | Fit | Residual | Standardized residual | Leverage |
|---|---|---|---|---|---|---|---|
| help-doe-getting-started-1 | 1 | Analyzed | 18.72 | 18.7872 | -0.0671591 | -0.165039 | 0.482955 |
| help-doe-getting-started-2 | 2 | Analyzed | 28.38 | 28.9097 | -0.529659 | -1.3016 | 0.482955 |
| help-doe-getting-started-3 | 3 | Analyzed | 17.82 | 17.6947 | 0.125341 | 0.308017 | 0.482955 |
| help-doe-getting-started-4 | 4 | Analyzed | 22.53 | 22.5542 | -0.0242424 | -0.0482605 | 0.212121 |
| help-doe-getting-started-5 | 5 | Analyzed | 22.09 | 22.5222 | -0.432159 | -1.062 | 0.482955 |
| help-doe-getting-started-6 | 6 | Analyzed | 21.89 | 22.5542 | -0.664242 | -1.32234 | 0.212121 |
| help-doe-getting-started-7 | 7 | Analyzed | 21.83 | 21.7897 | 0.0403409 | 0.099135 | 0.482955 |
| help-doe-getting-started-8 | 8 | Analyzed | 22 | 22.0097 | -0.00965909 | -0.0237365 | 0.482955 |
| help-doe-getting-started-9 | 9 | Analyzed | 20.45 | 20.2022 | 0.247841 | 0.609052 | 0.482955 |
| help-doe-getting-started-10 | 10 | Analyzed | 28.89 | 28.8922 | -0.00215909 | -0.00530581 | 0.482955 |
| help-doe-getting-started-11 | 11 | Analyzed | 23.87 | 22.5542 | 1.31576 | 2.61934 | 0.212121 |
| help-doe-getting-started-12 | 12 | Analyzed | 20.68 | 20.8703 | -0.190341 | -0.467749 | 0.482955 |
| help-doe-getting-started-13 | 13 | Analyzed | 23.47 | 23.2224 | 0.247576 | 0.49286 | 0.212121 |
| help-doe-getting-started-14 | 14 | Analyzed | 18.18 | 18.3628 | -0.182841 | -0.449319 | 0.482955 |
| help-doe-getting-started-15 | 15 | Analyzed | 22.32 | 23.2224 | -0.902424 | -1.7965 | 0.212121 |
| help-doe-getting-started-16 | 16 | Analyzed | 29.62 | 29.5603 | 0.0596591 | 0.146608 | 0.482955 |
| help-doe-getting-started-17 | 17 | Analyzed | 30.05 | 29.5778 | 0.472159 | 1.1603 | 0.482955 |
| help-doe-getting-started-18 | 18 | Analyzed | 19.58 | 19.4553 | 0.124659 | 0.306341 | 0.482955 |
| help-doe-getting-started-19 | 19 | Analyzed | 22.63 | 22.6778 | -0.0478409 | -0.117566 | 0.482955 |
| help-doe-getting-started-20 | 20 | Analyzed | 23.25 | 23.2224 | 0.0275758 | 0.0548963 | 0.212121 |
| help-doe-getting-started-21 | 21 | Analyzed | 22.36 | 22.4578 | -0.0978409 | -0.240437 | 0.482955 |
| help-doe-getting-started-22 | 22 | Analyzed | 23.68 | 23.1903 | 0.489659 | 1.2033 | 0.482955 |
Factor coding
Factor names the input and Type its modeling type. Center and Scale translate numeric settings to coded values: (setting − center) / scale. Thus the midpoint is 0 and the entered low/high bounds are −1/+1. Levels / contrasts applies to categorical coding; a dash is not a missing numeric measurement. Keep the model-column, block and rank notes with this table.
| Factor | Type | Center | Scale | Levels / contrasts |
|---|---|---|---|---|
| jaw_temperature_c | numeric | 160 | 10 | — |
| dwell_time_s | numeric | 1 | 0.2 | — |
| jaw_pressure_mpa | numeric | 0.3 | 0.05 | — |
- Model columns: Intercept, jaw_temperature_c, dwell_time_s, jaw_pressure_mpa, jaw_temperature_c × dwell_time_s, jaw_temperature_c × jaw_pressure_mpa, dwell_time_s × jaw_pressure_mpa, Block · contrast 1, Center point
- Rank tolerance: 1e-10
- Block level: Day_1
- Block level: Day_2
Coefficient covariance
Read each row and column term together. Diagonal entries are the squared standard errors of the fitted coefficients. Off-diagonal entries describe shared estimation uncertainty. This matrix concerns model coefficients, not correlations between the measured factor columns.
| Column | Intercept | jaw_temperature_c | dwell_time_s | jaw_pressure_mpa | jaw_temperature_c × dwell_time_s | jaw_temperature_c × jaw_pressure_mpa | dwell_time_s × jaw_pressure_mpa | Block · contrast 1 | Center point |
|---|---|---|---|---|---|---|---|---|---|
| Intercept | 0.0200165 | 0 | 0 | 0 | -1.73724e-18 | 0 | 0 | 0 | -0.0200165 |
| jaw_temperature_c | 0 | 0.0200165 | 1.25524e-18 | 1.59056e-18 | -2.37535e-18 | 1.14682e-18 | 6.87283e-19 | -3.11116e-19 | 2.40441e-19 |
| dwell_time_s | 0 | 1.25498e-18 | 0.0200165 | 1.41339e-18 | -8.20222e-18 | 2.83927e-18 | -2.97871e-18 | 9.96778e-18 | 8.55081e-21 |
| jaw_pressure_mpa | 0 | 1.34066e-18 | 1.85008e-18 | 0.0200165 | -8.38039e-19 | 1.83585e-19 | -4.22472e-18 | -8.36686e-18 | 4.86775e-20 |
| jaw_temperature_c × dwell_time_s | -1.73724e-18 | -1.7558e-18 | -8.74062e-18 | -7.0199e-19 | 0.0200165 | -2.49201e-18 | 6.54714e-18 | -4.5524e-18 | 4.71332e-18 |
| jaw_temperature_c × jaw_pressure_mpa | 0 | 1.09564e-18 | 2.83401e-18 | 3.04389e-19 | -1.87779e-18 | 0.0200165 | 8.66089e-19 | -4.98088e-19 | -6.83801e-21 |
| dwell_time_s × jaw_pressure_mpa | 0 | 1.56378e-19 | -2.08591e-18 | -3.66915e-18 | 7.17073e-18 | 5.66413e-19 | 0.0200165 | 1.36697e-18 | 2.63412e-19 |
| Block · contrast 1 | 0 | -3.11116e-19 | 9.96778e-18 | -8.36686e-18 | -4.5524e-18 | -4.98088e-19 | 1.36697e-18 | 0.0145575 | 4.24889e-34 |
| Center point | -0.0200165 | 2.40441e-19 | 8.55081e-21 | 4.86775e-20 | 4.71332e-18 | -6.83801e-21 | 2.63412e-19 | 4.24889e-34 | 0.073394 |
Prediction and coefficient detail
PRESS sums leave-one-out prediction errors: each run is predicted by a model fitted without that run. Predicted R² uses those errors. Coefficient covariance records estimation uncertainty; its diagonal entries are squared coefficient standard errors. These diagnostics supplement, rather than replace, lack-of-fit and residual checks.
8. Create a report
Keep Model overview, Adjusted term ANOVA, Coefficients, Coefficient covariance, Row diagnostics and Factor coding, plus the Factorial effects table and effects and residual plots. Include the response units, factor settings, recorded run order and all model notes. Keep the lack-of-fit result with the residual checks; it does not validate the model on its own.
Choose Add to report from the completed run. Open Choose individual items and advanced options to select tables and charts, then choose Add to draft. Hidden items stay in the saved analysis.
Name the report and add the purpose of the study and your interpretation. Choose Save, review Preview, then use Export → Download HTML. The example below contains the full selected content, including results beyond one screen.