Summary: Basic DOE Method for Product Testing

Building on the solar car application, we can summarize the basic approach to design of experiments with full-factorial configurations. This approach utilizes the mathematical methods discussed in this section.

Step 1: Identify the performance variables (responses), design variables (control factors), and noise variables (uncontrolled factors). State all high-level physical principles to clarify and understand the product testing.

Step 2: Define the target values for the responses and boundaries for the design variables.

Step 3: Plan the prototype testing by developing an experimental matrix, choosing the number of trails, levels for each design variable, number of replicates, and how the response will be measured. In addition, determine the experimental apparatus and methods for eliminating noise sources.

Step 4: Execute experiments by randomizing the trails and replicates; record the data to the accuracy needed for analysis.

Step5: Analyze the results by constructing a regression model or response diagram(s). Calculate and average the variances of the replicates; determine the overall standard deviation from the average variance and compare the standard deviation to coefficients of the regression model. After determining the significant results, use the regression model and/or graphs to make design changes to the product.

III. STATISTICAL ANALYSIS OF EXPERIMENTS

When testing physical product prototypes, the regression fit (empirical model) must be statistically analyzed for confidence in the fit and significance of each design variable. There are at least five parameters that are useful:

1. standard error of the replicates

2. correlation coefficient of the fit

3. standard error of the residuals of the fit

4. t-ratio (t-statistic or t-test) of each variable of the fit or replicates

5. Analysis of Variance (ANOVA): F-ratio of the fit and replicates

Beyond calculating these values analytically, they may also be graphically determined, such as the concept of plotting the residuals. One can then visually examine plots for trends in the random data. We have previously discussed the standard error of the replicates; now we explore the remaining parameters. To define these parameters, however, we must first define statistical degrees of freedom.

Degrees of Freedom

A degree of freedom is the number of independent variables that contribute to a statistical quantity. Degrees of freedom are used to properly weight component variances into the summary quantities.

A set of nine experiments has nine degrees of freedom.

• The overall average, on the other hand, has one degree of freedom.
• The number of degrees of freedom associated with a variable d; is equal to one less than the number of levels M; for that variable (the one being subtracted for the average).
• The degree of freedom in a sum of squares is M - 1, where M is the number of elements in the sum. The -1 comes from the constraint that . Since the mean is subtracted, the value of y; is subtracted from itself, resulting in a loss of degree of freedom.
• The degrees of freedom associated with interaction effects are given by the products of the degrees of freedom for each of the two factors. That is, the degrees of freedom for the interaction effect between two variables a and b is

Date: 2016-01-14; view: 604