Weibull++ Equation Fit Solver Example: Difference between revisions
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{{Banner Weibull Examples}} | {{Banner Weibull Examples}} | ||
'''Weibull++ Equation Fit Solver Example''' | |||
The Equation Fit Solver can be used to perform linear and nonlinear regression. For example, assume that an engineer collected the following degradation data. | |||
{| | border="1" class="wikitable" style="margin: 1em auto 1em auto" | |||
| align="center" style="background:#f0f0f0;"|'''Time''' | |||
| align="center" style="background:#f0f0f0;"|'''Reading''' | |||
|- | |||
| 5||8.08 | |||
|- | |||
| 10||13.52 | |||
|- | |||
| 15||21.86 | |||
|- | |||
| 20||31.96 | |||
|- | |||
| 25||37.86 | |||
|- | |||
| 30||46.67 | |||
|- | |||
| 35||53.35 | |||
|- | |||
| 40||62.29 | |||
|- | |||
| 45||71.62 | |||
|- | |||
| 50||80.37 | |||
|- | |||
| 55||91.43 | |||
|- | |||
| 60||104.00 | |||
|} | |||
From the physical mechanism, the engineer knows that the degradation path follows the following equation: | |||
::<math>y=a+bx+c\ln (x)</math> | |||
where: <br> | |||
*x is the time | |||
*y is the degradation reading. | |||
This model is not a standard degradation model in Weibull++; however, the problem can be solved by using the Equation Fit Solver. | |||
'''Solution:''' | |||
'''Step 1:''' Insert an Equation Fit Solver folio in your project and enter the given data in the folio, as shown next. | |||
[[Image: Equation Fit Solver Data.png|thumb|center|400px]] | |||
'''Step 2:''' Enter the degradation equation in the control panel and name it “My Degradation Equation,” as shown next. | |||
[[Image: Equation Fit Solver Function.png|thumb|center|400px]] | |||
'''Step 3:''' Click '''Calculate'''. The following picture shows the results. | |||
[[Image: Equation Fit Solver Result.png|thumb|center|400px]] | |||
'''Step 4:''' You can use the '''Calculate Y given X''' area on the control panel to make predictions. For example, the predicted Y value at X=100 is 176.2424. | |||
[[Image: Equation Fit Solver Prediction.png|thumb|center|400px]] | |||
'''Step 5:''' The following plot shows the fitted model and the observed values. | |||
[[Image: Equation Fit Solver Plot.png|thumb|center|400px]] |
Revision as of 07:26, 23 July 2012
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Weibull++ Equation Fit Solver Example
The Equation Fit Solver can be used to perform linear and nonlinear regression. For example, assume that an engineer collected the following degradation data.
Time | Reading |
5 | 8.08 |
10 | 13.52 |
15 | 21.86 |
20 | 31.96 |
25 | 37.86 |
30 | 46.67 |
35 | 53.35 |
40 | 62.29 |
45 | 71.62 |
50 | 80.37 |
55 | 91.43 |
60 | 104.00 |
From the physical mechanism, the engineer knows that the degradation path follows the following equation:
- [math]\displaystyle{ y=a+bx+c\ln (x) }[/math]
where:
- x is the time
- y is the degradation reading.
This model is not a standard degradation model in Weibull++; however, the problem can be solved by using the Equation Fit Solver.
Solution:
Step 1: Insert an Equation Fit Solver folio in your project and enter the given data in the folio, as shown next.
Step 2: Enter the degradation equation in the control panel and name it “My Degradation Equation,” as shown next.
Step 3: Click Calculate. The following picture shows the results.
Step 4: You can use the Calculate Y given X area on the control panel to make predictions. For example, the predicted Y value at X=100 is 176.2424.
Step 5: The following plot shows the fitted model and the observed values.