The same logic in the Duane model is followed here. If Eqn. 1 is linearized,
According to Crow [9], the likelihood function for the grouped data case, where n1, n2, n3,..., nk failures are observed and k is the number of groups, is:
And the MLE of 
based on this relationship
is:
(32)
And the estimate of 
is the value 
that satisfies:
(33)
Consider the Grouped Failure Times data given in Table 5.2. Solve for the Crow-AMSAA parameters using MLE.
Table 5.2 - Grouped Failure Times data
|
Run Number |
Cumulative Failures |
End Time (hr) |
ln (Ti) |
ln (Ti)2 |
|
|
|
1 |
2 |
200 |
5.298 |
28.072 |
0.693 |
3.673 |
|
2 |
3 |
400 |
5.991 |
35.898 |
1.099 |
6.582 |
|
3 |
4 |
600 |
6.397 |
40.921 |
1.386 |
8.868 |
|
4 |
11 |
3000 |
8.006 |
64.102 |
2.398 |
19.198 |
|
|
|
Sum = |
25.693 |
168.992 |
5.576 |
38.321 |
To obtain the estimator of 
, Eqn. 33
must be solved numerically for 
. Using RGA,
the value of 
is 0.6315. Now plugging this
value into Eqn. 32, the estimator of 
is:
Therefore, the intensity function becomes:
See
Also:
Crow-AMSAA (N.H.P.P.)
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