Designing an Experiment

Overview

DOE (design of experiments) helps you investigate the effects of input variables (factors) on an output variable (response) at the same time. These experiments consist of a series of runs, or tests, in which purposeful changes are made to the input variables. Data are collected at each run. You use DOE to identify the process conditions and product components that affect quality, and then determine the factor settings that optimize results.

Minitab offers five types of designs: screening designs, factorial designs, response surface designs, mixture designs, and Taguchi designs (also called Taguchi robust designs). The steps you follow in Minitab to create, analyze, and visualize a designed experiment are similar for all types. After you perform the experiment and enter the results, Minitab provides several analytical tools and graph tools to help you understand the results. This chapter demonstrates the typical steps to create and analyze a factorial design. You can apply these steps to any design that you create in Minitab.

Minitab DOE commands include the following features:
  • Catalogs of designed experiments to help you create a design
  • Automatic creation and storage of your design after you specify its properties
  • Display and storage of diagnostic statistics to help you interpret the results
  • Graphs to help you interpret and present the results

In this chapter, you investigate two factors that might decrease the time that is needed to prepare an order for shipment: the order-processing system and the packing procedure.

The Western center has a new order-processing system. You want to determine whether the new system decreases the time that is needed to prepare an order. The center also has two different packing procedures. You want to determine which procedure is more efficient. You decide to perform a factorial experiment to test which combination of factors enables the shortest time that is needed to prepare an order for shipment.

Create a designed experiment

Before you can enter or analyze DOE data in Minitab, you must first create a designed experiment in the worksheet. Minitab offers a variety of designs.

Screening
Includes definitive screening and Plackett-Burman designs.
Factorial
Includes 2-level full designs, 2-level fractional designs, split-plot designs, and Plackett-Burman designs.
Response surface
Includes central composite designs and Box-Behnken designs.
Mixture
Includes simplex centroid designs, simplex lattice designs, and extreme vertices designs.
Taguchi
Includes 2-level designs, 3-level designs, 4-level designs, 5-level designs, and mixed-level designs.

You choose the appropriate design based on the requirements of your experiment. Choose the design from the Stat > DOE menu. You can also open the appropriate toolbar by choosing Tools > Toolbars. After you choose the design and its features, Minitab creates the design and stores it in the worksheet.

Select a design

You want to create a factorial design to examine the relationship between two factors, order-processing system and packing procedure, and the time that is needed to prepare an order for shipping.

  1. Choose File > New > Project.
  2. Choose Stat > DOE > Factorial > Create Factorial Design.
    When you create a design in Minitab, only two buttons are enabled, Display Available Designs and Designs. The other buttons are enabled after you complete the Designs sub-dialog box.
  3. Click Display Available Designs.
    For most design types, Minitab displays all the possible designs and the number of required experimental runs in the Display Available Designs dialog box.
  4. Click OK to return to the main dialog box.
  5. Under Type of Design, select 2-level factorial (default generators).
  6. From Number of factors, select 2.
  7. Click Designs.
    The area at the top of the sub-dialog box shows available designs for the design type and the number of factors that you chose. In this example, because you are performing a factorial design with two factors, you have only one option, a full factorial design with four experimental runs. A 2-level design with two factors has 22 (four) possible factor combinations.
  8. From Number of replicates for corner points, select 3.
  9. Click OK to return to the main dialog box. All the buttons are now enabled.

Enter the factor names and set the factor levels

Minitab uses the factor names as the labels for the factors on the analysis output and graphs. If you do not enter factor levels, Minitab sets the low level at −1 and the high level at 1.

  1. Click Factors.
  2. In the row for Factor A, under Name, enter OrderSystem. Under Type, select Text. Under Low, enter New. Under High, enter Current.
  3. In the row for Factor B, under Name, enter Pack. Under Type, select Text. Under Low, enter A. Under High, enter B.
  4. Click OK to return to the main dialog box.

Randomize and store the design

By default, Minitab randomizes the run order of all design types, except Taguchi designs. Randomization helps ensure that the model meets certain statistical assumptions. Randomization can also help reduce the effects of factors that are not included in the study.

Setting the base for the random data generator ensures that you obtain the same run order each time you create the design.

  1. Click Options.
  2. In Base for random data generator, enter 9.
  3. Verify that Store design in worksheet is selected.
  4. Click OK in each dialog box.

View the design

Each time you create a design, Minitab stores design information and factors in worksheet columns.

  1. Maximize the worksheet to see the structure of a typical design.

The RunOrder column (C2) indicates the order to collect data. If you do not randomize the design, the StdOrder and RunOrder columns are the same.

In this example, because you did not add center points or put runs into blocks, Minitab sets all the values in C3 and C4 to 1. The factors that you entered are stored in columns C5 (OrderSystem) and C6 (Pack).

Note

You can use Stat > DOE > Display Design to switch between a random display and a standard-order display, and between a coded display and an uncoded display. To change the factor settings or names, use Stat > DOE > Modify Design. If you need to change only the factor names, you can enter them directly in the worksheet.

Enter data into the worksheet

After you perform the experiment and collect the data, you can enter the data into the worksheet.

The characteristic that you measure is called a response. In this example, you measure the number of hours that are needed to prepare an order for shipment. You obtain the following data from the experiment:

14.72 9.62 13.81 7.97 12.52 13.78 14.64 9.41 13.89 13.89 12.57 14.06

  1. In the worksheet, click the column name cell of C7 and enter Hours.
  2. In the Hours column, enter the data as shown below.
    You can enter data in any columns except in columns that contain design information. You can also enter multiple responses for an experiment, one response per column.
Note

To print a data collection form, click in the worksheet and choose File > Print Worksheet. Verify that Print Grid Lines is selected. Use the form to record measurements during the experiment.

Analyze the design

After you create a design and enter the response data, you can fit a model to the data and generate graphs to assess the effects. Use the results from the fitted model and graphs to determine which factors are important to reduce the number of hours that are needed to prepare an order for shipment.

Fit a model

Because the worksheet contains a factorial design, Minitab enables the DOE > Factorial menu commands, Analyze Factorial Design and Factorial Plots. In this example, you fit the model first.

  1. Choose Stat > DOE > Factorial > Analyze Factorial Design.
  2. In Responses, enter Hours.
  3. Click Terms. Verify that A:OrderSystem, B:Pack, and AB are in the Selected Terms box.
    When you analyze a design, always use the Terms sub-dialog box to select the terms to include in the model. You can add or remove factors and interactions by using the arrow buttons. Use the check boxes to include blocks and center points in the model.
  4. Click OK.
  5. Click Graphs.
  6. Under Effects Plots, select Pareto and Normal.
    Effects plots are available only in factorial designs. Residual plots, which you use to verify model assumptions, can be displayed for all design types.
  7. Click OK in each dialog box.
    Minitab fits the model that you defined in the Terms sub-dialog box, displays the results in the Session window, and stores the model in the worksheet file. After you identify an acceptable model, you can use the stored model to perform subsequent analyses.

Identify important effects

You use the Session window output and the two effects plots to determine which effects are important to your process. First, look at the Session window output.

Factorial Regression: Hours versus OrderSystem, Pack

Analysis of Variance Source DF Adj SS Adj MS F-Value P-Value Model 3 53.894 17.9646 40.25 0.000 Linear 2 44.915 22.4576 50.32 0.000 OrderSystem 1 28.768 28.7680 64.46 0.000 Pack 1 16.147 16.1472 36.18 0.000 2-Way Interactions 1 8.979 8.9787 20.12 0.002 OrderSystem*Pack 1 8.979 8.9787 20.12 0.002 Error 8 3.571 0.4463 Total 11 57.464
Model Summary S R-sq R-sq(adj) R-sq(pred) 0.668069 93.79% 91.46% 86.02%
Coded Coefficients Term Effect Coef SE Coef T-Value P-Value VIF Constant 12.573 0.193 65.20 0.000 OrderSystem 3.097 1.548 0.193 8.03 0.000 1.00 Pack -2.320 -1.160 0.193 -6.01 0.000 1.00 OrderSystem*Pack 1.730 0.865 0.193 4.49 0.002 1.00
Regression Equation in Uncoded Units Hours = 12.573 + 1.548 OrderSystem - 1.160 Pack + 0.865 OrderSystem*Pack
Alias Structure Factor Name A OrderSystem B Pack
Aliases I A B AB
You fit the full model, which includes the two main effects and the 2-way interaction. Effects are statistically significant when their p-values in the Coded Coefficients table are less than α. At the default α of 0.05, the following effects are significant:
  • The main effects for the order-processing system (OrderSystem) and the packing procedure (Pack)
  • The interaction effect of the order-processing system and the packing procedure (OrderSystem*Pack)

Interpret the effects plots

You can also evaluate the normal probability plot and the Pareto chart of the standardized effects to see which effects influence the response, Hours.

  1. To view the normal probability plot, choose Window > Effects Plot for Hours.

    Square symbols identify significant terms. OrderSystem (A), Pack (B), and OrderSystem*Pack (AB) are significant because their p-values are less than the α of 0.05.

  2. To view the Pareto chart, choose Window > Effects Pareto for Hours.

    Minitab displays the absolute value of the effects on the Pareto chart. Any effects that extend beyond the reference line are significant. OrderSystem (A), Pack (B), and OrderSystem*Pack (AB) are all significant.

Use the stored model for additional analyses

You identified a model that includes the significant effects, and Minitab stored the model in the worksheet. A check mark in the heading of the response column indicates that a model is stored and it is up to date. Hold the pointer over the check mark to view a summary of the model.

You can use the stored model to perform additional analyses to better understand your results. Next, you create factorial plots to identify the best factor settings, and you use Minitab's Predict analysis to predict the number of hours for those settings.

Create factorial plots

You use the stored model to create a main effects plot and an interaction plot to visualize the effects.

  1. Choose Stat > DOE > Factorial > Factorial Plots.
  2. Verify that the variables, OrderSystem and Pack, are in the Selected box.
  3. Click OK.

Interpret the factorial plots

The factorial plots include the main effects plot and the interaction plot. A main effect is the difference in the mean response between two levels of a factor. The main effects plot shows the means for Hours using both order-processing systems and the means for Hours using both packing procedures. The interaction plot shows the impact of both factors, order-processing system and packing procedure, on the response. Because an interaction means that the effect of one factor depends on the level of the other factor, assessing interactions is important.

  1. To view the main effects plot, choose Window > Main Effects Plot for Hours.

    Each point represents the mean processing time for one level of a factor. The horizontal center line shows the mean processing time for all runs. The left panel of the plot indicates that orders that were processed using the new order-processing system took less time than orders that were processed using the current order-processing system. The right panel of the plot indicates that orders that were processed using packing procedure B took less time than orders that were processed using packing procedure A.

    If there were no significant interactions between the factors, a main effects plot would adequately describe the relationship between each factor and the response. However, because the interaction is significant, you should also examine the interaction plot. A significant interaction between two factors can affect the interpretation of the main effects.

  2. Choose Window > Interaction Plot for Hours to make the interaction plot active.

    Each point in the interaction plot shows the mean processing time at different combinations of factor levels. If the lines are not parallel, the plot indicates that there is an interaction between the two factors. The interaction plot indicates that book orders that were processed using the new order-processing system and packing procedure B took the fewest hours to prepare (9 hours). Orders that were processed using the current order-processing system and packing procedure A took the most hours to prepare (approximately 14.5 hours). Because the slope of the line for packing procedure B is steeper, you conclude that the new order-processing system has a greater effect when packing procedure B is used instead of packing procedure A.

    Based on the results of the experiment, you recommend that the Western shipping center use the new order-processing system and packing procedure B to decrease the time to deliver orders.

Predict the response

You determined the best settings, which are stored in the DOE model in the worksheet. You can use the stored model to predict the processing time for these settings.

  1. Choose Stat > DOE > Factorial > Predict.
  2. Under OrderSystem, select New.
  3. Under Pack, select B.
  4. Click OK.

Prediction for Hours

Regression Equation in Uncoded Units Hours = 12.573 + 1.548 OrderSystem - 1.160 Pack + 0.865 OrderSystem*Pack
Variable Setting OrderSystem New Pack B
Fit SE Fit 95% CI 95% PI 9 0.385710 (8.11055, 9.88945) (7.22110, 10.7789)

Interpret the results

The Session window output displays the model equation and the variable settings. The fitted value (also called predicted value) for these settings is 9 hours. However, all estimates contain uncertainty because they use sample data. The 95% confidence interval is the range of likely values for the mean preparation time. If you use the new order-processing system and packing procedure B, you can be 95% confident that the mean preparation time for all orders will be between 8.11 and 9.89 hours.

Save the project

  1. Choose File > Save Project As.
  2. Browse to the folder that you want to save your files in.
  3. In File name, enter MyDOE.
  4. Click Save.

In the next chapter

The factorial experiment indicates that you can decrease the time that is needed to prepare orders at the Western shipping center by using the new order-processing system and packing procedure B. In the next chapter, you learn how to use command language and create and run exec files to quickly re-run an analysis when new data are collected.

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