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 &amp; 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:

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

$$R(t)=e^{\big({t \over \eta}\big)^\beta}$$

then for 0.85%,

$$1-0.0085=e^{\big({t \over 100}\big)^2}$$

and so forths as shown in the table below:

9.25 25.48 40.77 56.26 73.60 96.64

33.99 55.42 73.97 92.96 115.33 148.84

70.66 93.37 114.21 136.98 166.34 218.32