New format available! This reference is now available in a new format that offers faster page load, improved display for calculations and images and more targeted search.
As of January 2024, this Reliawiki page will not continue to be updated. Please update all links and bookmarks to the latest references at RGA examples and RGA reference examples.
Multiple Systems (Known Operating Times) Data Reference Example
|
This example compares the results for multiple systems (known operating times) data.
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: