Power-law projection

Duane MTBF Projection Calculator

Project cumulative MTBF and the corresponding instantaneous MTBF at a future cumulative test time.

Projection inputs

Use a future time at or beyond the baseline and a fitted slope below 1.

What this calculator does

It extends one baseline cumulative-MTBF point along a Duane log-log growth line and reports the modeled cumulative value. The result message also reports the instantaneous value at that future time.

When to use it

Use it to compare a planned future test milestone with the current growth model. Treat it as a conditional forecast that must be refreshed with actual failure and corrective-action data.

Inputs and formula

The same time unit must be used for both test-time fields and MTBF. A β of zero produces no modeled growth; β approaching 1 produces a widening difference between cumulative and instantaneous MTBF.

Cumulative MTBF(T) = baseline MTBF × (T ÷ baseline time)^β; instantaneous MTBF(T) = cumulative MTBF(T) ÷ (1 − β)

Worked example and interpretation

A 50-hour cumulative MTBF at 100 test hours, β of 0.4, and future time of 400 hours project about 87.06 hours cumulative MTBF and 145.10 hours instantaneous MTBF.

Practical notes and limitations

The formula assumes the fitted power-law trend continues. It does not include uncertainty, fix delays, reliability jumps, test phase boundaries, or a finite failure-mode ceiling. Never present the instantaneous value as the observed average interval.