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Multiple Systems - Known Operating Times
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This example validates the results for multiple systems (known operating times) data in RGA.
Reference Case
MIL-HDBK-189A, Section 6.3.1.6.4, pg. 156, 2009.
For this example, the following will be calculated:
- Parameters of the Crow-AMSAA (NHPP) model
- Demonstrated MTBF (DMTBF)
- Cramér-von Mises (CVM) goodness-of-fit
Data
The following table shows the data.
| Prototype #1
|
Prototype #2
|
Cumulative Time
|
| *2.6 |
0 |
2.6
|
| *16.5 |
0 |
16.5
|
| *16.5 |
0 |
16.5
|
| *17 |
0 |
17
|
| 20.5 |
*0.9 |
21.4
|
| 25.3 |
*3.8 |
29.1
|
| 28.7 |
*4.6 |
33.3
|
| *41.8 |
14.7 |
56.5
|
| *45.5 |
17.6 |
63.1
|
| 48.6 |
*22 |
70.6
|
| 49.6 |
*23.4 |
73
|
| *51.4 |
26.3 |
77.7
|
| *58.2 |
35.7 |
93.9
|
| 59 |
*36.5 |
95.5
|
| 60.5 |
*37.6 |
98.1
|
| *61.9 |
39.1 |
101.1
|
| *76.6 |
55.4 |
132
|
| 81.1 |
*61.1 |
142.2
|
| *84.1 |
63.6 |
147.7
|
| *84.7 |
64.3 |
149
|
| *94.6 |
72.6 |
167.2
|
| 104.8 |
*85.9 |
190.7
|
| 105.9 |
*87.1 |
193
|
| *108.8 |
89.9 |
198.7
|
| 132.4 |
*119.5 |
251.9
|
| 132.4 |
*150.1 |
282.5
|
| 132.4 |
*153.7 |
286.1
|
Termination Time = 300 hours
(* = system failed)
Result
The book has the following results:
- Beta = 0.716, Lambda = 0.454
- Using significance level = 0.05. CVM = 0.091. Critical value = 0.218. Since CVM < critical value can fail to reject hypothesis that model fits the data.
Results in RGA
In RGA, the Crow-AMSAA (NHPP) model with the maximum likelihood estimation (MLE) method was used to calculate the results.
- The model parameters are:
- The Cramér-von Mises (CVM) goodness-of-fit test results:
