Grouped Data Reference Example: Difference between revisions

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{{Reference Example|{{Banner RGA Reference_Examples}}}}
{{Reference Example|{{Banner RGA Reference_Examples}}|Grouped Data}}
This example compares the results for grouped data.  
This example validates the results for grouped data in RGA.  




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MIL-HDBK -189A, Section 6.3.1.7.5, pg. 162, 2009.
MIL-HDBK -189A, Section 6.3.1.7.5, pg. 162, 2009.
For this example, the following will be calculated:
*Parameters of the Crow-AMSAA (NHPP) model
*Demonstrated MTBF (DMTBF)
*Chi-squared goodness of fit




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*DMTBF = 2.6 hours
*DMTBF = 2.6 hours


*<math>\,\!X^{2}</math> = 5.5, critical value = 7.8 (Assume significance level = 0.1. Since <math>\,\!X^{2}</math> < critical value can fail to reject hypothesis that the Crow-AMSAA model fits the data).
*<math>\,\!\chi ^{2}</math> = 5.5, critical value = 7.8 (Assume significance level = 0.1. Since <math>\,\!\chi ^{2}</math> < critical value can fail to reject hypothesis that the Crow-AMSAA model fits the data).




{{Reference_Example_Heading4|RGA}}
{{Reference_Example_Heading4|RGA}}


In RGA, the Crow-AMSAA (NHPP) model with the maximum likelihood estimation (MLE) method was used to calculate the results:
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 model parameters are:
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*The chi-squared goodness-of-fit test result:
*The chi-squared goodness-of-fit test results:


[[image:MIL-HDBK-189A 6.3.1.7.5 Example_Stats.png|center]]
[[image:MIL-HDBK-189A 6.3.1.7.5 Example_Stats.png|center]]

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Grouped Data

This example validates the results for grouped data in RGA.


Reference Case

MIL-HDBK -189A, Section 6.3.1.7.5, pg. 162, 2009.

For this example, the following will be calculated:

  • Parameters of the Crow-AMSAA (NHPP) model
  • Demonstrated MTBF (DMTBF)
  • Chi-squared goodness of fit


Data

The following table shows the data.

Failures in Interval Interval End Time
13 20
16 40
5 60
8 80
7 100
Termination Time = 100 hours


Result

The book has the following results:

  • Beta = 0.753, Lambda = 1.53
  • DMTBF = 2.6 hours
  • [math]\displaystyle{ \,\!\chi ^{2} }[/math] = 5.5, critical value = 7.8 (Assume significance level = 0.1. Since [math]\displaystyle{ \,\!\chi ^{2} }[/math] < critical value can fail to reject hypothesis that the Crow-AMSAA 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 6.3.1.7.5 Example Results.png


  • The chi-squared goodness-of-fit test results:
MIL-HDBK-189A 6.3.1.7.5 Example Stats.png


  • Failure intensity vs. time plot:
MIL-HDBK-189A 6.3.1.7.5 Example Plot.png
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