# Using PTC Mathcad to isolate factors influencing your design

During the Singapore Grand Prix held last weekend, you couldn’t help but feel a sense of complete bafflement in the Mercedes grand prix pit as they struggled to make sense of the lack of performance from a car that has so far this season been streets ahead of the field. As you can well imagine there are a multitude of factors that can affect the setup of F1 cars for them to be ready to be pushed to their theoretical limits.

But which factors should they have focused on? During the race, commentators speculated and there was talk of the problem potentially being linked to tire pressure. What was the ideal tire pressure that would ensure perfect balance of the car? It would appear based on results that this question was mainly left unanswered. Mercedes had just experienced their worst weekend performance in a long time.

Being able to identify those key parameters is something that is crucial not only in fine tuning a race car, but also in engineering & delivering products with the best performance, quality and reliability.

“The challenge facing corporations is to cut design and development time while producing low-cost quality products that are ready to perform. Many organizations are being challenged to cut delivery time in half or more.” [2]

This ability to identify the key factors that have greatest impact on a design & development have been developed and fine-tuned over the years and comes from a well-known branch of study namely “Design of Experiments” or DOE for short.

So what of Design of Experiments and how does PTC Mathcad help engineers and designers improve their experiments? First thing to take note of is that PTC Mathcad has some useful capabilities for undertaking DOE studies. These begin with the generation of the design matrices which are necessary to determine the size and number of experiments or runs. PTC Mathcad’s capabilities further extend into Factor Screening, Analysis of Variance and Regression Analysis. 2D plots such as Pareto and Effects plots can be used to help visualise & make sense of the results of your experiments.

In order to put these capabilities in PTC Mathcad to the test, I approached our resident DOE expert Knud Nissen. To demonstrate what is possible we have an example of an automobile where we want to understand the factors that have greatest impact/influence on the mileage performance of the car. Having a range of both quantitative and qualitative factors to choose from, we will study the effect of 4 quantitative factors.

• Tire Pressure
• Ignition timing
• Oil Type
• Gas Type

The assumption is that each factor has 2 levels:

A – Tire Pressure:               28 psi   35 psi

B – Ignition Timing:            Low       High

C – Oil Type:                           1         2

D – Gas Type:                         1         2

With a selection of matrix functions to choose from a fractal factorial function was used to reduce the number of runs from 16 down to 8 thus saving valuable time and resources. The matrix and results are captured in an Excel component in PTC Mathcad to enhance the display of experimental matrix.

Using the effects trace in PTC Mathcad we can get a quick visual indication of those factors that we need to focus on. The steepness of the slope of the lines representing each factor reflect the importance of that factor in achieving the desired outcome.

It is apparent from the graph above that the most important effects are factor A and the interaction of AC. However with a resolution IV we find that AC is also aliased with BD. Therefore we must go back to the factors to determine which interaction is responsible for the steep slope. The steep slope is unlikely to be caused by the interaction of tire pressure & ignition timing (the AC interaction). Hence we may deduce that it must be due to the ignition timing & type of oil or the BD interaction.

We can further isolate the factors that will have the greatest impact on variability. This can be achieved by using the standard deviation instead of the mean values with the quickscreen function. It’s clear from the plot below that we should set the factor C at low level to reduce variability to ensure we have a robust design.

So there we have it, with the help of PTC Mathcad we have optimised the number of experimental runs and isolated the factors and their optimal levels that should help maximize the mileage of the car. We could extend this by calculating the half-effects and using the coefficients to produce the characteristic equation. With this equation we are able to predict the results for experiments we did not conduct when we originally set up the design matrix to be 8 runs rather than the full 16 runs.

If you are interested in the subject of Design of Experiments and want to better understand how PTC Mathcad can help devise your experiment, we provide you with the worksheet used in the example above here. This worksheet is based on an example from reference [1] below.