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Factorial Reliability Designs

Factorial Reliability Designs: Example

The data set used in this example is available in the example database installed with the software (called "DOE10_examples.rsgz10"). To access this database file, choose File > Help, click Open Examples Folder, then browse for the file in the DOE sub-folder.

The name of the example project is "Reliability DOE - Life Time Test of Fluorescent Lights."

In this example, two level factorial reliability DOE is used to determine the best factor settings to improve the reliability of fluorescent light bulbs. Five two-level factors were used in a fractional design to investigate the main effects of the factors and the interaction effect of the first two factors. It is assumed that none of the other interaction effects are significant and that the life of the bulb follows a lognormal distribution.

Each treatment in the design has two replicates (i.e., two bulbs were tested at each factor level combination), and the experiment was conducted over 20 days with inspections every two days. (The failure times were short because the lights were subjected to an accelerating factor that stressed the lights at higher than normal conditions.) Some of the units were still not failed at the end of the 20-day test.

Designing the Experiment

The design matrix and the response data are given in the "Fluorescent Light Life Test" folio. The following steps describe how to create this folio on your own.

Analysis and Results

The data set for this example is given in the "Fluorescent Light Life Test" folio of the example project. After you enter the data from the folio, you can perform the analysis by doing the following:

Note: To minimize the effect of unknown nuisance factors, the run order is randomly generated when you create the design in DOE++. Therefore, if you followed these steps to create your own folio, the order of runs on the Data tab may be different from that of the folio in the example file. This can lead to different results. To ensure that you get the very same results described next, show the Standard Order column in your folio, then click a cell in that column and choose Sheet > Sheet Actions > Sort > Sort Ascending. This will make the order of runs in your folio the same as that of the example file. Then copy the response data from the example file and paste it into the Data tab of your folio.

In the window that appears, select the Main Effects and A·B check boxes. Then click OK.

From the MLE Information table, you can see the model for the ln-mean or the scale parameter in the lognormal distribution is:

μ = 2.9392 + 0.1168A - 0.2015B - 0.051C - 0.2729D + 0.1527E - 0.0488AB

Then choose Pareto Charts - Regression from the Plot Type drop-down list. The following plot appears.

The horizontal blue line in the plot marks the critical value determined by the risk level specified on the Analysis Settings page of the control panel. If the bar goes past the blue line, then the effect is considered significant.

Conclusion

From the regression model, we can determine that in order to improve the reliability, factors B, C and D should be set to their low (-1) level, indicated by their negative coefficients, while A and E should be set at their high (+1) level, indicated by their positive coefficients. Under this setting, the predicted scale parameter in the lognormal distribution is 3.7829. Therefore, the life distribution under this factor setting is a lognormal distribution with a standard deviation of 0.1589 and ln-mean of 3.7829.

To do more advanced analysis, you can enter the data into ReliaSoft’s ALTA for accelerated life data analysis to further investigate the life stress relationship. Since factors A and C are not shown to be significant, they can be removed in further analysis.

 

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