Using MCF to derive MTBF

[ggross]

I have been using the Non-Parametric Recurrence Data Analysis feature in Weibull++ to analyze failure data on a fleet of repairable systems, using the Mean Cumulative Function. This results in a series of average number of service events for a given corresponding time period. I also wanted to compare the MCF with a standard cumulative MTBF calculation. In order to convert the MCF to MTBF, I divided the mid-point of each MCF time period by it's corresponding MCF data point. So for example if the MCF for time period 55 days through 65 days was 0.016 failures, then the corresponding MTBF at 60 days would be; MTBF (60 days) = 60 / 0.16 = 375 days.

Any comments on the validity of this?

[David]

The process that you are using is correct, although generally the endpoint is used instead of the midpoint. Also, keep in mind that there is cumulative MTBF and instantaneous MTBF. Your current method estimates the cumulative MTBF. The instantaneous MTBF can be calculated using the following:

Time = 0 to 10, MCF = 0.5
Time = 10 to 20, MCF = 0.8

The incremental change in MCF from 10 to 20 is equal to 0.8-0.5 = 0.3. The delta time is equal to 20-10 = 10. Therefore, the instantaneous failure rate is equal to 0.3/10 = 0.03.

The instantaneous MTBF = 1/0.03 = 33.333.

I hope this helps.

[ggross]

David,

Thanks for the additional information - much appreciated!