Cumulative vs Instantaneous MTBF

[john trinkle]

Can I please have a simple explanation of the difference between cumulative and instantaneous MTBF when using the RGA6 Crow-AMSAA (NHPP) model.

[adam]

The cumulative MTBF is the average TBF from the beginning of the test (i.e., t=0) up to time t. The instantaneous MTBF is average TBF in an interval dt. It is easier to understand when using Grouped data. Say you had 4 failures in the first interval 0-100 hrs and 2 failures in the second interval 100-180 hrs. The cumulative MTBF at 180 hrs of test time is 180/6=30, where your instantaneous is 80/2=40.

[john trinkle]

So if I have a Beta (using grouped data Crow-AMSAA) that is near 1, I should see a an instantaneous and cumulative MTBF vey near to each other. Otherwise the instantaneous and cumulative would be very different. Correct?

[tarik]

That is correct.
Having a beta >1 means that the system is degrading (IMTBF(t) is less than CMTBF(t)). Wherease a beta < 1 means that the system is improving (IMTBF(t) is greater than CMTBF(t)). So if beta = 1 than the system's MTBF is staying the same (IMTBF(t) = CMTBF(t)).

[Michael]

Is there a formula to calculate instantenous MTBF from Weibull parameters?
Is the cummulative MTBF always increasing while the failure rate is decresing? Why is this so.
Cheers

[tarik]

For the Crow-AMSAA (NHPP) model, the instantenous MTBF formulation can be found at:
http://www.weibull.com/RelGrowthWeb/n_h_h_p_.htm

[Pantelis]

MTBF or MTTF ... I think what you are looking for is MTTF. If so see http://www.weibull.com/LifeDataWeb/weibull_statistical_properties.htm