Expected Failure Time Plot: Difference between revisions

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<p><span class="fck_mw_template">{{UConstruction}}</span>
#REDIRECT [[Reliability_Test_Design#Expected_Failure_Times_Plots]]
</p>
<h1>Expected Failure Time Plot</h1>
<p>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.
</p>
<h2> Background &amp; Calculations  </h2>
<p>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:
</p><p><br />
</p>
<table border="1" cellspacing="1" cellpadding="1" width="400" align="center">
<caption> Table 1: 5%, 50% and 95% Ranks for a sample size of 6.&nbsp;
</caption>
<tr>
<th bgcolor="#cccccc" valign="middle" scope="col" align="center"> Order Number
</th><th bgcolor="#cccccc" valign="middle" scope="col" align="center"> 5%
</th><th bgcolor="#cccccc" valign="middle" scope="col" align="center"> 50%
</th><th bgcolor="#cccccc" valign="middle" scope="col" align="center"> 95%
</th></tr>
<tr>
<td valign="middle" align="center"> 1
</td><td valign="middle" align="center"> 0.85%
</td><td valign="middle" align="center"> 10.91%
</td><td valign="middle" align="center"> 39.30%
</td></tr>
<tr>
<td valign="middle" align="center"> 2
</td><td valign="middle" align="center"> 6.29%
</td><td valign="middle" align="center"> 26.45%
</td><td valign="middle" align="center"> 58.18%
</td></tr>
<tr>
<td valign="middle" align="center"> 3
</td><td valign="middle" align="center"> 15.32%
</td><td valign="middle" align="center"> 42.14%
</td><td valign="middle" align="center"> 72.87%
</td></tr>
<tr>
<td valign="middle" align="center"> 4
</td><td valign="middle" align="center"> 27.13%
</td><td valign="middle" align="center"> 57.86%
</td><td valign="middle" align="center"> 84.68%
</td></tr>
<tr>
<td valign="middle" align="center"> 5
</td><td valign="middle" align="center"> 41.82%
</td><td valign="middle" align="center"> 73.55%
</td><td valign="middle" align="center"> 93.71%
</td></tr>
<tr>
<td valign="middle" align="center"> 6
</td><td valign="middle" align="center"> 60.70%
</td><td valign="middle" align="center">
<p>89.09%
</p>
</td><td valign="middle" align="center">
<p>99.15%
</p>
</td></tr></table>
<p><br />
</p><p>Furthermore, consider that for the units to be tested the underlying reliability model assumption is given by a Weibull distribution with <span class="texhtml">&beta; = 2</span>, and <span class="texhtml">&eta; = 100</span> 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,
</p><p>or
</p><p><img _fckfakelement="true" _fck_mw_math="R(t)=e^{\big({t \over \eta}\big)^\beta}" src="/images/math/9/b/2/9b21aed609d5cefddaae485bbfbc3a2f.png" />
</p><p>then for 0.85%,
</p><p><br /><img _fckfakelement="true" _fck_mw_math="1-0.0085=e^{\big({t \over 100}\big)^2}" src="/images/math/d/b/e/dbe99885cf4bd0ea65638a820287544a.png" />
</p><p>and so forths as shown in the table below:
</p><p><br />
</p>
<table border="1" cellspacing="1" cellpadding="1" width="400" align="center">
 
<tr>
<th bgcolor="#cccccc" scope="col"> Failure Order Number
</th><th bgcolor="#cccccc" scope="col"> Lowest Expected Time-to-failure (hr)
</th><th bgcolor="#cccccc" scope="col"> Median Expected Time-to-failure (hr)
</th><th bgcolor="#cccccc" scope="col"> Highest Expected Time-to-failure (hr)
</th></tr>
<tr>
<td valign="middle" align="center"> 1
</td><td valign="middle" align="center"> 9.25
</td><td valign="middle" align="center"> 33.99
</td><td valign="middle" align="center"> 70.66
</td></tr>
<tr>
<td valign="middle" align="center"> 2
</td><td valign="middle" align="center"> 25.48
</td><td valign="middle" align="center"> 55.42
</td><td valign="middle" align="center"> 93.37
</td></tr>
<tr>
<td valign="middle" align="center"> 3
</td><td valign="middle" align="center"> 40.77
</td><td valign="middle" align="center"> 73.97
</td><td valign="middle" align="center"> 114.21
</td></tr>
<tr>
<td valign="middle" align="center"> 4
</td><td valign="middle" align="center"> 56.26
</td><td valign="middle" align="center"> 92.96
</td><td valign="middle" align="center"> 136.98
</td></tr>
<tr>
<td valign="middle" align="center"> 5
</td><td valign="middle" align="center"> 73.60
</td><td valign="middle" align="center"> 115.33
</td><td valign="middle" align="center"> 166.34
</td></tr>
<tr>
<td valign="middle" align="center"> 6
</td><td valign="middle" align="center">
<p>96.64
</p>
</td><td valign="middle" align="center"> 148.84
</td><td valign="middle" align="center"> 218.32
</td></tr></table>
<p><br /><br />
</p><p><br />
</p><p><br />
</p><p><br />
</p><p><br /><br />
</p><a _fcknotitle="true" href="Category:Weibull++">Weibull++</a> <a _fcknotitle="true" href="Category:Test_Design">Test_Design</a> <a _fcknotitle="true" href="Category:Special_Tools">Special_Tools</a>

Latest revision as of 22:51, 21 August 2012

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