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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 visual.
| | #REDIRECT [[Reliability_Test_Design#Expected_Failure_Times_Plots]] |
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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.
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| 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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| | 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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| |-
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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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| |-
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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.
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| 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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| <math>R(t)=e^{\big({t \over \eta}\big)^\beta}</math>
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| then for 0.85%,
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| <br><math>1-0.0085=e^{\big({t \over 100}\big)^2}</math>
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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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| |}
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| <br><br>
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| <br>
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| 9.25<br>25.48<br>40.77<br>56.26<br>73.60<br>96.64<br>
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| 33.99<br>55.42<br>73.97<br>92.96<br>115.33<br>148.84<br>
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| 70.66<br>93.37<br>114.21<br>136.98<br>166.34<br>218.32<br><br><br>
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| [[Category:Weibull++]] [[Category:Test_Design]] [[Category:Special_Tools]] | |