Example 11 - Two Level Fractional Factorial Reliability Design
[Download DOE++ Example File (*.rdoe)]
Background
Consider an experiment to improve the reliability of fluorescent lights. The purpose was to find the best factor setting to improve the life time. Five two-level factors denoted by A-E were studied using a 25-2 design with the factor generator D = AC and E = BC. In addition to the main effects, the experimenter also thought that the AB (= DE) interaction might be important.
Each treatment had two replicates (i.e. two lights were tested) 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). If a light had not failed by the 20th day, its failure time was recorded as right censored at 20.
Experiment Design
The engineer uses DOE++ to design a two level fractional factorial reliability design. The design-specific settings used are shown next.
The design matrix and the response data are given in the "Fluorescent Light Life Test" Folio.
Analysis
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: In the Select Effects window, the following effects are selected to include in the analysis:
Step 3: The Lognormal distribution is chosen for the analysis.
Step 4: The data set is analyzed with a risk (significance) level of 0.05, using individual terms. The model coefficients, shown in the MLE Information table on the Analysis tab, are:
Step 5: A Pareto chart is created, as shown next.
Conclusions
From the MLE Information table, it is determined that the model for the ln-mean or the scale parameter, m, in the distribution is:
The engineer determines 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 at their high (+1) level, indicated by their positive coefficients. This setting is also good for the AB interaction term. Under this setting, the predicted scale parameter in lognormal distribution is 3.7829. Therefore, the life distribution under this factor setting is a lognormal distribution with standard deviation of 0.1589 and ln-mean of 3.7829.
For more advanced analysis, the data can be entered into ReliaSoft’s ALTA for accelerated life data analysis for further investigation of the life stress relationship. Since factors A and C are not shown to be significant, they can be removed in further analysis.
