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= Expected Failure Time Plot  =
#REDIRECT [[Reliability_Test_Design#Expected_Failure_Times_Plots]]
 
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. Figure 1 below shows such a plot for h a sample size of 5 and an assumed Weibull distribution with β = 2 and η = 2,000 hrs and at a 90% confidence.
 
{| width="200" border="0" cellpadding="1" cellspacing="1" align="center" siber__q92dpb7seovvtbh5__vptr="7123c60" sourceindex="11"
|- siber__q92dpb7seovvtbh5__vptr="712a130" sourceindex="13"
| siber__q92dpb7seovvtbh5__vptr="71239d0" sourceindex="14" |
[[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 <span class="texhtml" siber__q92dpb7seovvtbh5__vptr="40bcc0" sourceindex="19">β = 2</span> and&nbsp;<span class="texhtml" siber__q92dpb7seovvtbh5__vptr="71034e0" sourceindex="20">η = 2,000</span> hrs and at a 90% confidence.
 
|- siber__q92dpb7seovvtbh5__vptr="7103710" sourceindex="21"
| siber__q92dpb7seovvtbh5__vptr="71037e0" sourceindex="22" |
|}
 
<br>
 
==Interpreting the EFT Plot==
 
<br>
 
== 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:
 
<br>
 
{| border="1" cellspacing="1" cellpadding="1" width="400" align="center" siber__q92dpb7seovvtbh5__vptr="71036b0" sourceindex="33"
|+ '''Table 1: 5%, 50% and 95% Ranks for a sample size of 6.&nbsp;'''
|- siber__q92dpb7seovvtbh5__vptr="71039e0" sourceindex="37"
! bgcolor="#cccccc" valign="middle" scope="col" align="center" siber__q92dpb7seovvtbh5__vptr="7103930" sourceindex="38" | Order Number
! bgcolor="#cccccc" valign="middle" scope="col" align="center" siber__q92dpb7seovvtbh5__vptr="7103100" sourceindex="39" | 5%
! bgcolor="#cccccc" valign="middle" scope="col" align="center" siber__q92dpb7seovvtbh5__vptr="7103760" sourceindex="40" | 50%
! bgcolor="#cccccc" valign="middle" scope="col" align="center" siber__q92dpb7seovvtbh5__vptr="71038b0" sourceindex="41" | 95%
|- siber__q92dpb7seovvtbh5__vptr="7103ad0" sourceindex="42"
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="71038c0" sourceindex="43" | 1
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103620" sourceindex="44" | 0.85%
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103a80" sourceindex="45" | 10.91%
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103a10" sourceindex="46" | 39.30%
|- siber__q92dpb7seovvtbh5__vptr="71035b0" sourceindex="47"
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103a00" sourceindex="48" | 2
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103b00" sourceindex="49" | 6.29%
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103970" sourceindex="50" | 26.45%
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103d90" sourceindex="51" | 58.18%
|- siber__q92dpb7seovvtbh5__vptr="7103c50" sourceindex="52"
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103be0" sourceindex="53" | 3
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103800" sourceindex="54" | 15.32%
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103d30" sourceindex="55" | 42.14%
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103b20" sourceindex="56" | 72.87%
|- siber__q92dpb7seovvtbh5__vptr="7103820" sourceindex="57"
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103de0" sourceindex="58" | 4
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103c60" sourceindex="59" | 27.13%
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103a50" sourceindex="60" | 57.86%
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103b10" sourceindex="61" | 84.68%
|- siber__q92dpb7seovvtbh5__vptr="7103fd0" sourceindex="62"
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103e90" sourceindex="63" | 5
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103c90" sourceindex="64" | 41.82%
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103a60" sourceindex="65" | 73.55%
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103f00" sourceindex="66" | 93.71%
|- siber__q92dpb7seovvtbh5__vptr="7103ff0" sourceindex="67"
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103db0" sourceindex="68" | 6
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103fe0" sourceindex="69" | 60.70%
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103f30" sourceindex="70" |
89.09%
 
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="71034b0" sourceindex="72" |
99.15%
 
|}
 
<br>
 
Furthermore, consider that for the units to be tested the underlying reliability model assumption is given by a Weibull distribution with <span class="texhtml" siber__q92dpb7seovvtbh5__vptr="7108080" sourceindex="77">β = 2</span>, and <span class="texhtml" siber__q92dpb7seovvtbh5__vptr="7108010" sourceindex="78">η = 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,
 
or
 
R(t)=e^{\big({t \over \eta}\big)^\beta}
 
then for 0.85%,
 
<br>1-0.0085=e^{\big({t \over 100}\big)^2}
 
<br>
 
and so forths as shown in the table below:
 
<br>
 
{| border="1" cellspacing="1" cellpadding="1" width="400" align="center" siber__q92dpb7seovvtbh5__vptr="71083a0" sourceindex="89"
|+ '''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" siber__q92dpb7seovvtbh5__vptr="71082e0" sourceindex="92">β = 2</span>, and <span class="texhtml" siber__q92dpb7seovvtbh5__vptr="7108200" sourceindex="93">η = 100</span> hr.'''
|- siber__q92dpb7seovvtbh5__vptr="7108490" sourceindex="95"
! bgcolor="#cccccc" scope="col" siber__q92dpb7seovvtbh5__vptr="71081a0" sourceindex="96" | Order Number
! bgcolor="#cccccc" scope="col" siber__q92dpb7seovvtbh5__vptr="71082b0" sourceindex="97" | Lowest Expected Time-to-failure (hr)
! bgcolor="#cccccc" scope="col" siber__q92dpb7seovvtbh5__vptr="7108500" sourceindex="98" | Median Expected Time-to-failure (hr)
! bgcolor="#cccccc" scope="col" siber__q92dpb7seovvtbh5__vptr="71085f0" sourceindex="99" | Highest Expected Time-to-failure (hr)
|- siber__q92dpb7seovvtbh5__vptr="7103d00" sourceindex="100"
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="71085e0" sourceindex="101" | 1
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7108530" sourceindex="102" | 9.25
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7103e10" sourceindex="103" | 33.99
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7108360" sourceindex="104" | 70.66
|- siber__q92dpb7seovvtbh5__vptr="71084b0" sourceindex="105"
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="71086d0" sourceindex="106" | 2
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="71084c0" sourceindex="107" | 25.48
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7108220" sourceindex="108" | 55.42
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7108680" sourceindex="109" | 93.37
|- siber__q92dpb7seovvtbh5__vptr="7108610" sourceindex="110"
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7108170" sourceindex="111" | 3
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7108600" sourceindex="112" | 40.77
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7108700" sourceindex="113" | 73.97
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7108570" sourceindex="114" | 114.21
|- siber__q92dpb7seovvtbh5__vptr="7108460" sourceindex="115"
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7108760" sourceindex="116" | 4
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7108910" sourceindex="117" | 56.26
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="71089e0" sourceindex="118" | 92.96
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="71084e0" sourceindex="119" | 136.98
|- siber__q92dpb7seovvtbh5__vptr="7108810" sourceindex="120"
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="71089a0" sourceindex="121" | 5
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7108400" sourceindex="122" | 73.60
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7108730" sourceindex="123" | 115.33
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="71088e0" sourceindex="124" | 166.34
|- siber__q92dpb7seovvtbh5__vptr="7108800" sourceindex="125"
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7108bd0" sourceindex="126" | 6
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7108a90" sourceindex="127" |
96.64
 
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="71088b0" sourceindex="129" | 148.84
| valign="middle" align="center" siber__q92dpb7seovvtbh5__vptr="7108b00" sourceindex="130" | 218.32
|}
 
<br><br>
 
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<br><br>
 
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Latest revision as of 22:51, 21 August 2012

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