# Example 10 - One Factor Reliability Design

## Background

One factor reliability DOE can be used in design comparison and factor effect identification.

Suppose that there are three different materials that can be used in a product. The engineer wants to know if there is a difference between these three choices and, if there is a difference, which material is the best choice in terms of the product life.

Ten samples were tested for each material. The test was stopped at 500 hours.

## Experiment Design

The engineer uses DOE++ to design a one factor reliability design. The design-specific settings and the factor properties used are shown next.

The design matrix and the response data are given in the "3 Levels One Factor" Folio..

## Analysis Part I

Step 1: After performing the experiment according to the design and recording the results, the engineer enters the data set into the Standard Folio, as shown next.

Step 2: The Weibull distribution is chosen for the analysis.

Step 3: The data set is analyzed with the default risk (significance) level of 0.1. The Likelihood Ratio Test table from the Analysis tab is shown next.

This table provides the test for the overall effect of the factor. A small p value indicates that the factor (treatment) has a significant effect on the response.

The second table is the MLE Information table, as shown next.

This table gives the value of the estimated parameters in the model. A small p value indicates that the parameter is significantly different from 0.

The third table, the Life Characteristic Summary table, displays the fitted life characteristic. For the Weibull distribution, the life characteristic is eta, the scale parameter, as shown next.

The last table, the Life Comparisons table, shows paired comparisons of the life at each level, as shown next.

Step 4: A Response vs. Level plot is created, as shown next.

From this plot, it is difficult to tell which material is the best.

Step 5: A Life Characteristic plot is created, as shown next.

This plot shows that material type C has the largest eta value, which means it has the longest expected life.

## Conclusions

The Likelihood Ratio Test Table shows that there is a significant difference between the three types of material. Most notably, from the paired comparison, it is apparent that there are significant differences between A and B and between A and C. The difference between B and C is not particularly significant.