Expected Failure Time Plot: Difference between revisions

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= 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 visual.  
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.  
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{| border="1" cellspacing="1" cellpadding="1" width="400" align="center"
{| border="1" cellspacing="1" cellpadding="1" width="400" align="center"
|+ Table 1: 5%, 50% and 95% Ranks for a sample size of 6.&nbsp;  
|+ '''Table 1: 5%, 50% and 95% Ranks for a sample size of 6.&nbsp;'''
|-
|-
! bgcolor="#cccccc" valign="middle" scope="col" align="center" | Order Number  
! bgcolor="#cccccc" valign="middle" scope="col" align="center" | Order Number  
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{| border="1" cellspacing="1" cellpadding="1" width="400" align="center"
{| border="1" cellspacing="1" cellpadding="1" width="400" align="center"
|+ Table 2: Times corresponding to the 5%, 50% and 95% Ranks for a sample size of 6. and assuming Weibull distribution with <span class="texhtml">β = 2</span>, and <span class="texhtml">η = 100</span> hr.;
|+ '''Table 2: Times corresponding to the 5%, 50% and 95% Ranks for a sample size of 6. and assuming Weibull distribution with <span class="texhtml">β = 2</span>, and <span class="texhtml">η = 100</span> hr.'''
|-
|-
! bgcolor="#cccccc" scope="col" | Failure Order Number  
! bgcolor="#cccccc" scope="col" | Order Number  
! bgcolor="#cccccc" scope="col" | Lowest Expected Time-to-failure (hr)  
! bgcolor="#cccccc" scope="col" | Lowest Expected Time-to-failure (hr)  
! bgcolor="#cccccc" scope="col" | Median Expected Time-to-failure (hr)  
! bgcolor="#cccccc" scope="col" | Median Expected Time-to-failure (hr)  

Revision as of 18:27, 2 March 2011

<IMG class=FCK__MWTemplate src="http://www.reliawiki.com/extensions/FCKeditor/fckeditor/editor/images/spacer.gif" width=1 height=1 _fckfakelement="true" _fckrealelement="0" _fck_mw_template="true">

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:


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

<img _fckfakelement="true" _fck_mw_math="R(t)=e^{\big({t \over \eta}\big)^\beta}" src="/images/math/9/b/2/9b21aed609d5cefddaae485bbfbc3a2f.png" />

then for 0.85%,


<img _fckfakelement="true" _fck_mw_math="1-0.0085=e^{\big({t \over 100}\big)^2}" src="/images/math/d/b/e/dbe99885cf4bd0ea65638a820287544a.png" />

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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