Expected Failure Time Plot
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 β = 2, and η = 100 hr.
Then the median time to failure of the first unit on test can be determined by solving the Weibull reliability equation for t, at each probability,
or
[math]\displaystyle{ R(t)=e^{\big({t \over \eta}\big)^\beta} }[/math]
then for 0.85%,
[math]\displaystyle{ 1-0.0085=e^{\big({t \over 100}\big)^2} }[/math]
and so forths as shown in the table below:
| Failure Order Number | Lowest Expected Time-to-failure (hr) | Median Expected Time-to-failure (hr) | Highest Expected Time-to-failure (hr) |
|---|---|---|---|
| 1 | 9.25 | 33.99 | 70.66 |
| 2 | 25.48 | 55.42 | 93.37 |
| 3 | 40.77 | 73.97 | 114.21 |
| 4 | 56.26 | 92.96 | 136.98 |
| 5 | 73.60 | 115.33 | 166.34 |
| 6 |
96.64 |
148.84 | 218.32 |