23 FACTORIAL DESIGN EXAMPLECollege of TechnologyDesign of Experiments

Most commonly used experimental designs in business are Full and Fractional factorial designs at two-levels and three-levels.

A full factorial designed experiment consists of all possible combinations of levels for all factors.

One of the assumptions we make for factors at 2-levels is that the response is approximately linear over the range of the factor settings chosen.

Example: A chemical reaction is dependent on 3-factors, temperature, pressure and time for reaction. The factors and their levels are shown in the table.

FactorsLow level -High level +temperature (T)80 deg.120 deg.pressure (P)50 units70 unitstime for reaction (R)5 min.15 min.

A 23 full factorial design was chosen to analyze all the main and 2-factor interactions. The response is the YIELD given as a percentage.

The questions that need to be answered are:Which main effects or interactions might affect the yield?Which main effects or interactions might influence variability in the yield?

In order to identify the significant main and interaction effects, a DOE layout was constructed as shown.

It shows the all the combinations of factors and their levels.

The responses (% yield) from the experiment are recorded (replicates).

DOE Experimental Layout

Factors/settings Response RunTPR % yield % yield1 805056159212050576783807052834412070551485805015252161205015444478070154550812070157174

We will use a simple program for calculations. Follow the EXCEL pages.

Go to the Factors & Design Matrix EXCEL worksheet and enter the factors & levels in yellow cells. As you enter the data, the table will be populated

Now go to the Data & StdDevs EXCEL worksheet . Enter the response data (% YIELD) in yellow cells. The table will be populated with avg., s.d., variance etc.

Now go to the Effects EXCEL worksheet . It gives the summary of calculations.

Go to the Effects DL EXCEL worksheet . DL is the decision limit, which is calculated to ease your pain!. It tells you the effects that was calculated in the previous table is significant or not? The number in the yellow cell is your value, 95% or 90% or 99%. We have taken 95% here.

Go to the Effects Pareto Scratch Pad EXCEL worksheet . It gives you the contribution each MAIN factor is responsible and INTERACTION effects

Go to the Effects Pareto EXCEL worksheet. This shows the effect of main factors & interactions and the decision limit. The decision limits line cuts main factors A &C, also the BC interaction.

Go to the Main Effects Charts EXCEL worksheet

Go to the Interaction Charts EXCEL worksheet

Go to the Interaction Charts EXCEL worksheet

For the HW assignment, you will be given triplicate data for 23 FACTORIAL DESIGN . Insert the third set of response data on the chart and repeat what we did in lectures. See assignment sheet.

*************