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| {{Reference_Example_Heading4|RGA}} | | {{Reference_Example_Heading4|RGA}} |
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| Since test-find-test, the assumption is <math>\,\!\beta =1</math>. Therefore:
| | In RGA, the Crow Extended model with the maximum likelihood estimation (MLE) method was used to calculate the results. |
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| | For a test-find-test, the assumption is <math>\,\!\beta =1</math>. Therefore: |
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| ::<math>\begin{align} | | ::<math>\begin{align} |
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| =&88.8889 | | =&88.8889 |
| \end{align}\,\!</math> | | \end{align}\,\!</math> |
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| | The model parameters are: |
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| [[image:IEC 61164 Example 4_Results.png|center]] | | [[image:IEC 61164 Example 4_Results.png|center]] |
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| | The growth potential MTBF plot: |
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| [[image:IEC 61164 Example 4_Plot.png|center|550px]] | | [[image:IEC 61164 Example 4_Plot.png|center|550px]] |
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Test-Find-Test Data Reference Example
|
This example compares the results for test-find-test data.
Reference Case
International Standard IEC 61164 (Reliability Growth in Product Design and Test – Statistical Test and Estimation Methods), Example 4, pg. 32.
Data
The following table shows the data.
| Failure Time
|
Classification Mode
|
| 150 |
BD1
|
| 253 |
BD2
|
| 475 |
BD3
|
| 540 |
BD4
|
| 564 |
BD5
|
| 636 |
A
|
| 722 |
BD5
|
| 871 |
A
|
| 996 |
BD6
|
| 1003 |
BD7
|
| 1025 |
A
|
| 1120 |
BD8
|
| 1209 |
BD2
|
| 1255 |
BD9
|
| 1334 |
BD10
|
| 1647 |
BD9
|
| 1774 |
BD10
|
| 1927 |
BD11
|
| 2130 |
A
|
| 2214 |
A
|
| 2293 |
A
|
| 2448 |
A
|
| 2490 |
BD12
|
| 2508 |
A
|
| 2601 |
BD1
|
| 2635 |
BD8
|
| 2731 |
A
|
| 2747 |
BD6
|
| 2850 |
BD13
|
| 3040 |
BD9
|
| 3154 |
BD4
|
| 3171 |
A
|
| 3206 |
A
|
| 3245 |
DB12
|
| 3249 |
BD10
|
| 3420 |
BD5
|
| 3502 |
BD3
|
| 3646 |
BD10
|
| 3649 |
A
|
| 3663 |
BD2
|
| 3730 |
BD8
|
| 3794 |
BD14
|
| 3890 |
BD15
|
| 3949 |
A
|
| 3952 |
BD16
|
Termination Time = 4000 hours
| BD Mode
|
EF
|
| 1 |
0.7
|
| 2 |
0.7
|
| 3 |
0.8
|
| 4 |
0.8
|
| 5 |
0.9
|
| 6 |
0.9
|
| 7 |
0.5
|
| 8 |
0.8
|
| 9 |
0.9
|
| 10 |
0.7
|
| 11 |
0.7
|
| 12 |
0.6
|
| 13 |
0.6
|
| 14 |
0.7
|
| 15 |
0.7
|
| 16 |
0.5
|
Result
The book has the following results:
- BetaBD (UnB) = 0.7472, LambdaBD = 0.0326
- Unseen BD Mode Failure Intensity = 0.0030/hr
- Goodness of fit for BD modes: CVM = 0.085, critical value = 0.171 with significance level = 0.1. Since CVM < critical value can fail to reject hypothesis that the model fits the data.
Results in RGA
In RGA, the Crow Extended model with the maximum likelihood estimation (MLE) method was used to calculate the results.
For a test-find-test, the assumption is [math]\displaystyle{ \,\!\beta =1 }[/math]. Therefore:
- [math]\displaystyle{ \begin{align}
DMTBF=&\frac{T}{N}\\
\\
=&\frac{4000}{45}\\
\\
=&88.8889
\end{align}\,\! }[/math]
The model parameters are:
- [math]\displaystyle{ \begin{align}
\lambda _{p}=&\lambda _{A}+\sum_{i=1}^{N_{BD}}\left ( 1-d_{i} \right )\lambda _{i}+\bar{d}h\left ( T \right )\\
\\
=&\frac{N_{A}}{T}+\sum_{i=1}^{N_{BD}}\left ( 1-d_{i} \right )\frac{N_{i}}{T}+\bar{d}\lambda _{BD}\beta _{BD}T^{\beta -1}\\
\\
=&\frac{13}{4000}+0.002+\left ( 0.7188 \right )\left ( 0.032572 \right )\left ( 0.74715 \right )\left ( 4000 \right )^{0.7472-1}\\
\\
=&0.007398\\
\\
PMTBF=&\frac{1}{\lambda _{p}}\\
\\
=&135.17
\end{align}\,\! }[/math]
The growth potential MTBF plot:
