# Grouped Data Reference Example

 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
• $\,\!\chi ^{2}$ = 5.5, critical value = 7.8 (Assume significance level = 0.1. Since $\,\!\chi ^{2}$ < 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:

• The chi-squared goodness-of-fit test results:

• Failure intensity vs. time plot: