Grouped Data Reference Example

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Grouped Data

This example validates the results for grouped data in RGA.

Reference Case

MIL-HDBK -189A, Section, 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


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


The book has the following results:

  • Beta = 0.753, Lambda = 1.53
  • DMTBF = 2.6 hours
  • [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).

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 Example Results.png

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

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