Use Math Models & Designed Experiments to Understand Your Design
Invest in the following steps to truly understand how and why your designs work.
1) Establish Technical Requirements with targets and ranges of desired performance.
- These bound our expectation of the Ys in the Y=f(Xs) relationship models that are to be "fitted" to our concepts.
2) Develop multiple concepts at the appropriate level in the product's hierarchical architecture.
- Use the Pugh Process to evaluate, hybridize and select the most feasible concept using a reasonable subset across your technical requirements derived in Step 1.
3) Construct a math model to explain each major and subordinate function within the concept.
- Define Y=f(Xs) models.
- Solve the equation(s) deterministically first to match the Y to the technical requirement target.
- Then, if acceptable, run the equation using a monte carlo simulation to establish ranges of acceptable performance across the technical requirement's tolerance range.
- Identify magnitude and direction of DY/DXi sensitivities that govern the utility of the equation.
- Identify equations or subsets of the equations that are suspicious, doubtful or loaded with risky assumptions.
- Identify functions that are too difficult model with first principles mathematics.
4) Design and build adjustable, modular proto types that are easy to change with regard to their controllable X parameters and factors.
5) Certify capable measurement systems for use during designed experimentation cycles on the proto types.
- Conduct Linearity, Bias, Stability, Resolution, P-T and Gage R&R studies.
6) Apply Designed Experiments to vary the Xs and measure the effect on Ys.
- Obtain data and analyze using ANOVA and Factorial Plotting
- Construct the Empirical Y=f(Xs) model using the results
7) Compare the math model of the Y=f(Xs) to DOE model; iterate to drive agreement.
Now you have a math model that explains how and why your design works on a parametric/factorial basis. The trick is to decide when to limit analytical modeling and rely mostly on DOE-based empirical modeling. A balanced and reasoned use of both analytical and empirical modeling is the safest and most efficient approach to building deep understanding right the first time. Product lifecycle management is easier when these models are in harmony and communicated clearly to the downstream owners of the product and its subordinate designs.
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