Expected Failure Time Plot

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 a visual.

Expected Failure Time Plot with a sample size of 5, an assumed Weibull distribution with b=2 and h-1,500 hrs and at a 90% confidence. Fig. 1: Expected Failure Time Plot with a sample size of 5, an assumed Weibull distribution with [math]\displaystyle{ \beta=2 }[/math] and[math]\displaystyle{ \eta=2,000 }[/math] hrs and at a 90% confidence.

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:

Table 1: 5%, 50% and 95% Ranks for a sample size of 6. 

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

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:

Table 2: Times corresponding to the 5%, 50% and 95% Ranks for a sample size of 6. and assuming Weibull distribution with β = 2, and η = 100 hr.

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

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