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| {| class="FCK__ShowTableBorders" border="0" cellspacing="0" cellpadding="0" align="center"; style="width:100%;"
| | #REDIRECT [[Weibull%2B%2B_Examples]] |
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| | valign="middle" align="left" bgcolor=EEEDF7|[[Image: Weibull-Examples-banner.png|400px|center]]
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| |}<br>
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| Five turbine blades were tested for crack propagation. The test units are cyclically stressed and inspected every 100,000 cycles for crack length. Failure is defined as a crack of length 30mm or greater.
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| Following is a table of the test results:
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| <center><math>\begin{matrix}
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| Cycles (x1000) & Unit A (mm)& Unit B (mm) & Unit C (mm) & Unit D (mm)& Unit E (mm) \\
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| 100 & 15 & 10 & 17 & 12 & 10 \\
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| 200 & 20& 15 & 25 & 16 & 15 \\
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| 300 & 22 & 20 &26 & 17 & 20 \\
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| 400 & 26 &25 & 27 & 20 & 26 \\
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| 500 & 29 & 30 & 33 &26 & 33 \\
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| \end{matrix}</math></center>
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| Using degradation analysis with an exponential model for the extrapolation, determine the B10 life for the blades.
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| '''Solution'''
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| The first step is to solve the equation <math>y=b\cdot {{e}^{a\cdot x}}</math> for <math>a</math> and <math>b</math> for each of the test units. Using regression analysis, these values for each of the test units are:
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| <center><math>\begin{matrix}
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| {} & a & b \\
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| Unit A & 0.00158 & 13.596 \\
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| Unit B & 0.00271 & 8.272 \\
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| Unit C & 0.00140 & 16.435 \\
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| Unit D & 0.00177 & 10.361 \\
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| Unit E & 0.00294 & 7.931 \\
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| \end{matrix}</math></center>
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| These results are shown graphically in the next figure.
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| <math></math>
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| [[Image:Degradation Example 1 Plot.png|thumb|center|400px| ]]
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| These values can now be substituted into the underlying exponential model, solved for <math>x</math> or:
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| <center><math>x=\frac{\text{ln}(y)-\text{ln}(b)}{a}</math></center>
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| Using the values of <math>a</math> and <math>b</math> , with <math>y=30</math> , the resulting time at which the crack length reaches 30mm is then found for each sample:
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| <center><math>\begin{matrix}
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| {} & Cycles-to-Failure \\
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| Unit A & \text{500,622} \\
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| Unit B & \text{475,739} \\
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| Unit C & \text{428,739} \\
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| Unit D & \text{600,810} \\
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| Unit E & \text{452,832} \\
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| \end{matrix}</math></center>
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| These times-to-failure can now be analyzed in the conventional manner. Assuming a two-parameter Weibull distribution and using the MLE estimation method, the distribution parameters are calculated as <math>\beta =8.055</math> and <math>\eta =519,555.</math> Using these values, the B10 life is calculated to be 392,918 cycles. The degradation analysis tool in Weibull++ performs this type of analysis for you. The following figure shows the data as entered in Weibull++ for this analysis.
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| <math></math>
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| [[Image:Degradation Example 1 Data and Result.png|thumb|center|400px| ]]
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