Multiple Systems (Known Operating Times) Data Reference Example

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Multiple Systems - Known Operating Times

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
  • DMTBF = 15.5 hours
  • 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:
MIL-HDBK-189A 6.3.1.6.4 Example Results.png


  • The Cramér-von Mises (CVM) goodness-of-fit test results:
MIL-HDBK-189A 6.3.1.6.4 Example Stat Tests.png