Expected Failure Time Plot: Difference between revisions
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solving for t, | solving for t, | ||
<math>R(t)=e^{\big({t \over \eta}\big)^\beta}</math> | <math>R(t)=e^{\big({t \over \eta}\big)^\beta}</math> | ||
<math>0.50=e^{\big({t \over 100}\big)^2}</math> | |||
<math>ln(0.50)=2 \big({t \over 100}\big)}</math> | |||
Revision as of 17:24, 14 February 2011
When a reliability life test is planned it is useful to visualize the expected outcome of the experiment. The Expected Failure Time Plot (introduced by ReliaSoft in Weibull++ 8)provides such visual.
Background & Calculations
Using the cumulative binomial, for a defined sample size, one can compute a rank (Median Rank if at 50% probability) for each ordered failure.
As an example and for a sample size of 6 the 5%, 50% and 95% ranks would be as follows:
| Order Number | 5% | 50% | 95% |
|---|---|---|---|
| 1 | 0.85% | 10.91% | 39.30% |
| 2 | 6.29% | 26.45% | 58.18% |
| 3 | 15.32% | 42.14% | 72.87% |
| 4 | 27.13% | 57.86% | 84.68% |
| 5 | 41.82% | 73.55% | 93.71% |
| 6 | 60.70% |
89.09% |
99.15% |
Furthermore, consider that for the units to be tested the underlying reliability model assumption is given by a Weibull distribution with [math]\displaystyle{ \beta=2 }[/math], and [math]\displaystyle{ \eta=100 }[/math] hr.
Then the median time to failure of the first unit on test can be determined by solving for t, [math]\displaystyle{ R(t)=e^{\big({t \over \eta}\big)^\beta} }[/math]
[math]\displaystyle{ 0.50=e^{\big({t \over 100}\big)^2} }[/math]
[math]\displaystyle{ ln(0.50)=2 \big({t \over 100}\big)} }[/math]