Multiple Response Optimization

Summary

Determines the optimal settings in an experiment with a single output, or with multiple competing outputs. It also provides a graphical tool for exploring what-if alternative solutions. A desirability function is created for each process output, with multiple outputs combined into an overall desirability using adjustable weights for each output.

Answers the questions:
  • In a designed experiment investigating the effects of process inputs on a single process output, what settings of the key inputs result in the optimal process output?
  • In a designed experiment investigating the effects of process inputs on two or more potentially competing process outputs, what settings of the key inputs provides the best compromise solution for all outputs?
  • If I change one or more inputs from the optimal solution, what happens to the individual outputs and how does it affect the compromise?
When to Use Purpose
Mid-project Very useful for determining the settings of key process inputs that result in the optimal value of a single process output.
Mid-project Very useful for determining the settings of key process inputs that result in the best compromise solution for satisfying the goals relative to two or more process outputs.
Mid-project Make adjustments to the initial optimal solution, determine the impact on the outputs and the compromise, and settle on a final optimal solution.

Data

Input is a 2K DOE, response surface DOE, or a mixture DOE solved for one or more outputs

How-To

  1. Design your DOE and collect data on all outputs of interest for each run.
  2. Analyze (reduce to final model) the DOE for each output. Minitab remembers the final model run for each output.
  3. For each output, select the goal to be achieved: maximize, minimize, or set on target.
    • If you are maximizing an output, specify a target (a goal) and a lower bound (the minimum acceptable value).
    • If you are minimizing an output, specify a target (a goal) and upper bound (the maximum acceptable value).
    • If you are setting an output to a target, specify the target, a lower bound (minimum acceptable value), and an upper bound (maximum acceptable value).
  4. For each output, establish weights and importance, which are used to fine tune the algorithm for selecting the best balanced solution. Weights determine how close you must be to the target to obtain the maximum benefit for a particular output. Importance values reflect the relative values of achieving the goals for each of the competing outputs. A high importance value means that it is more important to achieve the goals for a particular output.
  5. Adjust settings of the inputs as desired, until you settle on a final solution.

Guidelines

  • Ensure all output models have been reduced to their final state.
  • If you want to improve the mean and reduce variation (a common case of potentially competing outputs) with a 2K full or fractional factorial DOE, you can run the DOE for the mean response and then analyze the DOE for variation using Stat > DOE > Factorial > Analyze Variability or Stat > DOE > Factorial > Pre-Process Responses for Analyze Variability.
  • If your DOE is a 2K full or fractional factorial, be careful how you move factor settings using the interactive graph produced by the optimizer. The optimizer allows you to select any value of a numeric factor (not just the low or high settings used in the experiment). If you have not tested for curvature (with center points), selecting a value between the low and high settings of a factor could be dangerous, as the model is relying on linearity to calculate a predicted Y at the selected setting. If you added center points to the DOE and the curvature test is negative, then it is okay to select factor settings between the low and high settings used in the experiment.
  • If you have discrete numeric data from which you can obtain every equally spaced value and you have measured at least 10 possible values, you can evaluate these data as if they are continuous.

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