Duane trend estimate

Reliability Growth Slope Calculator

Estimate the log-log slope β between two positive cumulative test-time and cumulative-MTBF observations.

Two observation points

The later cumulative time must exceed the earlier time.

What this calculator does

It calculates the slope of the straight line connecting two cumulative-MTBF observations on logarithmic axes. The result is a simple two-point diagnostic, not a statistical fit.

When to use it

Use it for a transparent cross-check or an early planning estimate when only two consistent cumulative observations are available. Fit the full ordered failure-time dataset when it is available.

Inputs and formula

Both points must use the same system, configuration, test clock, and failure definition. The later time must exceed the earlier time; MTBF values must be positive.

β = ln(later cumulative MTBF ÷ earlier cumulative MTBF) ÷ ln(later test time ÷ earlier test time)

Worked example and interpretation

Moving from 50 hours cumulative MTBF at 100 test hours to 87.06 hours at 400 test hours gives β ≈ 0.4000. Values between 0 and 1 indicate an improving standard Duane trend; zero indicates no growth and negative values indicate deterioration between the points.

Practical notes and limitations

Two endpoints can hide reversals, clustered failures, phase changes, or periods with no effective corrective action. A slope at or above 1 is outside the usual improving power-law range and should trigger data and boundary review rather than automatic extrapolation.