Expected Failure Time Plot: Difference between revisions

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| [[Image:EFTP1.png|border|center|700px|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.]]
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[[Image:EFTP1.png|border|center|700px|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>\beta=2</math> and<math>\eta=2,000</math> hrs and at a 90% confidence.
 
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Revision as of 11:27, 10 March 2011

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.

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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