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| = Expected Failure Time Plot =
| | #REDIRECT [[Reliability_Test_Design#Expected_Failure_Times_Plots]] |
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| 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.
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| {| width="200" border="0" cellpadding="1" cellspacing="1" align="center"
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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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| '''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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| <br>
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| <br>
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| <br>
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| == Background & Calculations ==
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| 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:
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| <br>
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| {| border="1" cellspacing="1" cellpadding="1" width="400" align="center"
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| |+ '''Table 1: 5%, 50% and 95% Ranks for a sample size of 6. '''
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| ! bgcolor="#cccccc" valign="middle" scope="col" align="center" | Order Number
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| ! bgcolor="#cccccc" valign="middle" scope="col" align="center" | 5%
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| ! bgcolor="#cccccc" valign="middle" scope="col" align="center" | 50%
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| ! bgcolor="#cccccc" valign="middle" scope="col" align="center" | 95%
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| |-
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| | valign="middle" align="center" | 1
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| | valign="middle" align="center" | 0.85%
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| | valign="middle" align="center" | 10.91%
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| | valign="middle" align="center" | 39.30%
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| | valign="middle" align="center" | 2
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| | valign="middle" align="center" | 6.29%
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| | valign="middle" align="center" | 26.45%
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| | valign="middle" align="center" | 58.18%
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| | valign="middle" align="center" | 3
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| | valign="middle" align="center" | 15.32%
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| | valign="middle" align="center" | 42.14%
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| | valign="middle" align="center" | 72.87%
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| | valign="middle" align="center" | 4
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| | valign="middle" align="center" | 27.13%
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| | valign="middle" align="center" | 57.86%
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| | valign="middle" align="center" | 84.68%
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| | valign="middle" align="center" | 5
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| | valign="middle" align="center" | 41.82%
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| | valign="middle" align="center" | 73.55%
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| | valign="middle" align="center" | 93.71%
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| | valign="middle" align="center" | 6
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| | valign="middle" align="center" | 60.70%
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| | valign="middle" align="center" |
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| 89.09%
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| | valign="middle" align="center" |
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| 99.15%
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| |}
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| <br>
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| Furthermore, consider that for the units to be tested the underlying reliability model assumption is given by a Weibull distribution with <span class="texhtml">β = 2</span>, and <span class="texhtml">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,
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| or
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| R(t)=e^{\big({t \over \eta}\big)^\beta}
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| then for 0.85%,
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| <br>1-0.0085=e^{\big({t \over 100}\big)^2}
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| <br>
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| and so forths as shown in the table below:
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| <br>
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| {| border="1" cellspacing="1" cellpadding="1" width="400" align="center"
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| |+ '''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.'''
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| ! bgcolor="#cccccc" scope="col" | Order Number
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| ! bgcolor="#cccccc" scope="col" | Lowest Expected Time-to-failure (hr)
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| ! bgcolor="#cccccc" scope="col" | Median Expected Time-to-failure (hr)
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| ! bgcolor="#cccccc" scope="col" | Highest Expected Time-to-failure (hr)
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| | valign="middle" align="center" | 1
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| | valign="middle" align="center" | 9.25
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| | valign="middle" align="center" | 33.99
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| | valign="middle" align="center" | 70.66
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| | valign="middle" align="center" | 2
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| | valign="middle" align="center" | 25.48
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| | valign="middle" align="center" | 55.42
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| | valign="middle" align="center" | 93.37
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| |-
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| | valign="middle" align="center" | 3
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| | valign="middle" align="center" | 40.77
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| | valign="middle" align="center" | 73.97
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| | valign="middle" align="center" | 114.21
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| |-
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| | valign="middle" align="center" | 4
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| | valign="middle" align="center" | 56.26
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| | valign="middle" align="center" | 92.96
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| | valign="middle" align="center" | 136.98
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| | valign="middle" align="center" | 5
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| | valign="middle" align="center" | 73.60
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| | valign="middle" align="center" | 115.33
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| | valign="middle" align="center" | 166.34
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| | valign="middle" align="center" | 6
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| | valign="middle" align="center" |
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| 96.64
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| | valign="middle" align="center" | 148.84
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| | valign="middle" align="center" | 218.32
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| |}
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| <br><br>
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| <br>
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| <br>
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| <br>
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| <br><br>
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| <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>
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