What is the difference between cumulative and instantaneous MTBF?
The cumulative MTBF is the average time-between-failure from the beginning of the test (i.e. t=0) up to time t. The instantaneous MTBF is the average time-between-failure in a given interval, dt. It is easier to understand when considering grouped data. For example, 4 failures are found in the interval 0-100 hours and 2 failures are found in the second interval 100-180 hours. The cumulative MTBF at 180 hours of test time is equal to 180/6 = 30 hours. However, the instantaneous MTBF is equal to 80/2 = 40 hours.
When beta is equal to one, the system's MTBF is not changing over time; therefore, the cumulative MTBF equals the instantaneous MTBF. If beta is greater than one, then the system's MTBF is decreasing over time and the cumulative MTBF is greater than the instantaneous MTBF. If beta is less than one, then the system's MTBF is increasing over time and the cumulative MTBF is less than the instantaneous MTBF.
In regards to life data analysis, what type of analysis can be done when all of the data is suspended?
When the data set contains only suspensions, all you really know is that nothing failed by time T. This can be useful in determining an estimate of the reliability at time T. What may be of particular interest is how you obtain a model (i.e. fit a distribution to the data) for interpolation/extrapolation purposes. Trying to fit a two or three parameter Weibull model is not possible because there are no failures in the data set, and therefore you cannot fit a model that assumes a time varying failure rate. One option is to fit an exponential distribution and assume a constant failure rate. This will provide results; however, extrapolating beyond time T should be done with caution, especially with the constant failure rate assumption. A better option is to utilize a one parameter Weibull distribution. This requires that you assume a value for beta (shape parameter) from past designs, engineering knowledge, etc. Then the value of eta (scale parameter) can be estimated based on the assumed value of beta.
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