Three Level Compromise Test Plan for One Stress
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This example compares the statistically optimum test plan result for one stress from the ALTA Test Plan tool.
Reference Case
The data set is from Example 20.5 on page 542 in the book Statistical Methods for Reliability Data by Dr. Meeker and Dr. Escobar, John Wiley & Sons, 1998.
Data
A Weibull distribution with Arrhenius relationship is used. The Arrhenius relationship uses the following formula:
- [math]\displaystyle{ ln(\eta) = \beta_{0} + \beta_{1} \times \frac{11605}{T}\,\! }[/math]
The planning values of the model parameters used in the test plan are [math]\displaystyle{ \beta\,\! }[/math] = 1.667, [math]\displaystyle{ \beta_{0}\,\! }[/math] = -16.7333 and [math]\displaystyle{ \beta_{1}\,\! }[/math] = 0.7265. These planning values were obtained based on the following assumptions: 0.1% of the units will fail in 6 months (183 hours) at 50°C, and 90% would fail in 6 months at 120°C. This information is given in Example 20.2 on page 535.
The use temperature is 50°C (323.15°K) and the highest temperature used in the test is 120°C (393.15 °K).
A total of 300 units are available for testing. Three temperature levels can be used and 20% of the units will be tested at the middle temperature level. The objective of the test plan is to:
- Determine the three temperature levels used in the test.
- Determine the number of test units at the high and the low temperature level.
Tests will be conducted using the created test plan. The failure data from the test is then used to estimate the model parameters and the reliability model is used to predict the B10 life at 50°C and its variance.
We need to find a test plan with three temperature levels that will minimize the estimation variance for the B10 life at 50°C.
Result
The three level compromise test plan is:
- 156 units will be tested at temperature of 78°C (351.15°K)
- 60 units will be tested at temperature of 98°C (371.15°K)
- 84 units will be tested at temperature of 120°C (393.15°K)
The estimated standard error for the B10 life at 50°C from this test plan is [math]\displaystyle{ Ase\left [log \left(\hat{t}_{0.1}(50) \right) \right]\,\! }[/math] .
Results in ALTA