Grouped Data Reference Example

From ReliaWiki
Jump to navigation Jump to search
RGA Reference Examples Banner.png


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]\,\!\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 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