Design of Experiments Guide • Accelerated Life Test Designs • Example
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Example
This example shows how to use the Accelerated Life Test Design to augment an existing design.
An accelerated life test was performed, and the results are in the Capacitor ALT.jmp sample data table (in the Design Experiment folder). Fifty units were tested at each of three temperatures (85o, 105o, and 125o Celsius) for 1500 hours. The resulting model is used to predict the probability of failure at 100,000 hours at normal use conditions of 25o.
1.
Select Help > Sample Data Library and open Design Experiment/Capacitor ALT.jmp.
2.
Run the Fit Life by X table script.
3.
In the Distribution Profiler, enter 25 for Temp and 100,000 for Hours.
The profiler is shown in Distribution Profiler for Capacitor Model.
Distribution Profiler for Capacitor Model
The predicted probability of failure at 100,000 hours at 25o is 0.00358, with a confidence interval of 0.00056 to 0.0227. The analyst wants to decrease the width of the confidence interval. To do so, the experiment needs to be augmented with additional data.
To augment the design in the optimal way, use the Accelerated Life Test Design platform. Follow the steps below to use the platform:
1.
Select DOE > Accelerated Life Test Design.
2.
Select Design for one accelerating factor and click Continue.
3.
Enter Temperature for Factor Name.
4.
Enter 5 for Number of Levels.
5.
Enter 25 for both Low Usage Condition and High Usage Condition.
6.
Click Continue.
7.
Enter 85, 95, 105, 115, and 125 for the Temperature Level Values.
8.
Select Weibull for Distribution Choice.
9.
Under Prior Mean, enter the acceleration model parameters from the Fit Life by X Estimates report. See Fit Life by X Estimates.
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Enter -35.200 for Intercept.
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Enter 1.389 for Temperature.
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Enter 1.305 for scale.
Fit Life by X Estimates
In the Fit Life by X output, under the Estimates report, is the Covariance Matrix report. Note the variances for the acceleration model parameters are 22, 0.025, and 0.013. These values will be compared to our final results at the end.
10.
Enter 100,000 for both boxes for Time range of interest.
11.
Enter 1500 for Length of Test.
12.
Enter 300 for Number of Units Under Test. The previous experiment used 150 units, and the next experiment uses 150 units, for a total of 300.
The completed window is shown in Completed Window.
Completed Window
13.
Click Continue.
14.
To account for the units in the previous experiment, enter the following under Candidate Runs.
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Enter 50 for Minimum Units for 85o.
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Enter 50 for Minimum Units for 105o.
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Enter 50 for Minimum Units for 125o.
15.
From the red triangle menu for Accelerated Life Test Plan, select ALT Optimality Criterion > Make Probability I-Optimal Design.
16.
Click Make Design.
The optimal experimental design is returned, along with other results. See Optimal Design.
Optimal Design
The optimal design is computed based on the Number of Units Under Test, Candidate Runs, and other information that you specified earlier. The optimal design consists of the following number of units at each temperature level:
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184 units at 85o. Since the previous experiment used 50 units, 134 additional units are needed.
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0 units at 95o. The next experiment will not utilize any units at this level.
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50 units at 105o. Since the previous experiment already used 50 units, no additional units are needed.
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0 units at 115o. The next experiment will not utilize any units at this level.
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66 units at 125o. Since the previous experiment used 50 units, 16 additional units are needed.
As we entered earlier, a total of 134+16=150 units are used for the new experiment.
An estimate of the acceleration model parameters variances is given. Note that, due to the additional data, all three variances are smaller than before from the original Fit Life by X report.
In the Profiler, enter 25 for Temperature and 100,000 for Time. The estimated probability of failure is 0.00357, with an estimated confidence interval of 0.00106 to 0.01201. This interval is narrower than the one from the previous experiment, as a result of the additional units to be tested.
To decrease the interval further, try entering more than 300 units to be tested.