## 5. Design of Experiments (DOE)

• WHAT? combinations of individual parameters for process control are varied, and their effect on output quantities are measured. From this we determine the sensitivity of the process to each parameter.

• WHY? Because randomly varying (trial and error) individual parameters takes too long and the results are not mathematically conclusive.

5.1 OVERVIEW

• The basic process for analysis is shown below. • The purpose of DOE is to prove a relationship between given outputs and inputs. Cases that are possible include:

no relationship

positive relationship

negative relationship

interaction between inputs

• e.g. A One-Factor-At-A-Time-Experiment • The example shows how the number of samples grows quickly.

• A better approach is designed experiments

5.2 n-Factorial

• These experiments vary parameters with the basic procedure below,

1. Identify process variables (inputs) and dependant variables (outputs). Outputs should be continuous values.

2. Select discrete values for the inputs. The most basic approach is to pick a high and low value for each.

3. Create a data collection table that has parameters listed (high/low) in a binary sequence. Some of these tests can be left off (fractional factorial experiment) if some relationships are known to be insignificant or irrelevant.

4. Run the process using the inputs in the tables. Take one or more readings of the output variable(s). If necessary, average the output values for each of the experiments.

5. Graph the responses varying only one of the process parameters. This will result in curves that agree or disagree. If the curves agree then the conclusion can be made that process variables are dependent. In this case the relationship between these variables requires further study.

6. Calculate the effects of the process variable change.

7. Use the results of the experiment to set process parameters, redesign the process, or to design further experiments.

• e.g. 3-factorial DOE for springs in last section     5.3 Problems

Problem 5.1 You have collected the data below as part of a 2-n factorial experiment for making slush. There are two process variables you control, a quantity of sugar and a quantity of salt that is added to the water, these modify the freezing temperature of the slush. Draw effects graphs and calculate the effects of changing the parameters. State whether they are dependent or independent.  