This chapter will present an illustration of the DOE process in a worked example that the reader can follow and execute themselves. All steps in the DOE process are executed. A numerical simulation tool is used as the test article that the reader can access if they want to reproduce the results and use this chapter as a Tutorial. The presented analysis is done in MiniTAB with the execution steps documented. Imagine yourself for a moment employed in the military over 1,000 years ago. Your job, as an
“Ingeniator” (engineer), is to determine the optimal setup for a newly designed siege weapon called a “Ingenium” or “trebuchet” (see illustration at the right), which harnesses the potential energy of a suspended weight to throw objects great distances. Advanced scouting has determined that in the next upcoming siege your trebuchet can be safely positioned in a wooded area outside the Evil Emperior’s castle of the SixSigma Dynasty. Your Commanding Officer and his System’s Engineering Lieutenant gives you the assignment of determining all the trebuchet’s critical factors and their associated settings to consistently hit a range of 390 to 410 feet, the anticipated requirement to smash the castle walls. The Quality Officer goes on to further define
“consistently” as missing less than 1 time in 100 attempts. Your mission, as you therefore understand it, is to flow an Upper Level Requirement (range within target of 390-410 feet 99% of the time) into Lower Level Specifications for the trebuchet design and settings. After consulting with
fellow Ingeniators, you discover that no one has an analytical model to predict the trebuchet’s distance as a function of settings, but everyone has their opinion of what are the most critical and useful adjustments. Problem is, there is no
agreement among the experts and no one has any data to defend their viewpoint. Based on careful considerations, you decide to perform DOE testing to answer your CO’s request.
You hold a meeting with your fellow Ingeniators and talk about what factors influence the range of the trebuchet’s toss. As you feared there a many variables to consider. In the end your
list includes nine potential control factors (see the
diagram at the right). Three weight values are considered (W1-W3), five dimensions (L1-L4 and H), and one
geometric variable (RA). Only one output response is considered, the horizontal distance the object travels. [At this point you hope that
there are no other walls which must be cleared to hit the castle wall.] So, you are done with DOE Step 1, the process diagram with 9 inputs (some of which might be considered noise factors at a later time) and 1 response is set.
The next step is to formulate the test matrix and plans. Clearly the first step in testing should be to narrow down the set of factors which must be considered (see Figure 2.1) so a
Screening DOE is recommended. A Placket-Burman design is chosen and can be created using MiniTAB using the pulldown menus as illustrated below.
You then select the Placket-Burman design with 9 factors using the popup menu, click OK and then accept the default parameters (0 corner points and only 1 replicate, this is sufficient for a Screening DOE). Next you must enter the factor names and variable ranges. The Screening DOE will use only 2 levels, so a High
and Low value must be used. The factor information entered by clicking on the “Factors” button. For this particular case it was decided that the Low levels would be at a baseline setting and High values would be a 10% increase in the factor levels. Finally, you can choose to randomize or not randomize the order that the test runs are stored. Here, by clicking on “Options” and unchecking the option “Randomize Runs”, and then clicking OK you will end up with the Screening DOE test
matrix as illustrated in Figure 5.1.
Now we are ready to execute the tests on the trebuchet. Before conducting the actual tests a Gage R&R analysis must be performed to ensure that the measurement system is adequate for the testing. MiniTAB provides tools to perform this analysis. A few test runs on made with the trebuchet at its nominal settings. Initially it was considered that fellow Ingeniators could stand out on the firing range and drop stones where they thought the 500 lb. projectile first hit. A calibrated string (a precursor to our modern
tape measures) was then used to measure the shot distance. Results indicated a sta
Rather than construct your own trebuchet, the user can use a trebuchet projectile prediction tool (Trebuchet for Windows V2.0 by Major Stephen J.
Ressler from West Point) that has been constructed using numerical simulation. The GUI for this simulation is the illustration used earlier to define the trebuchet factors. The measured distance for this Screening DOE test is listed in the test matrix in Figure 5.1.
A simple analysis can be performed in MiniTAB to identify the most significant factors. The Main Effects plot, as shown in Figure 5.2, shows three control factors are most significant – the release angle (RA), the length of the arm (L1), and the sling length (L4). This result was interesting, many of the Ingeniators were convinced their adjustment recommendations were right, but after reviewing this data and its systematic analysis they agreed with the conclusions. Surprisingly many were sure that
the projectile weight was critical to the range, but this testing refuted that claim.
Having reduced the number of control factors to 3, the next step is to construct a new Modeling DOE design. It is not known if interactions and nonlinearities are significant, so a Box-Behnken design is created (using the recommendations from Figure 2.1). Nominal values for the other control factors were set as follows: W1=11,000lbs, W2=6,200lbs, W3=500lbs, L2=29ft, L3=23ft, and H=25ft. The developed DOE design is shown in
Figure 5.3. In MiniTAB you can select the Box-Behnken design using the pull-down menu sequence STAT>DOE>Response Surface>Create Response
Surface Design. You can then select the Box-Behnken option, define the factors and levels and a test matrix will be automatically generated.