What is Reliability Growth? During the flight test development phase of new aircraft or early service entry of components, design engineering teams identify failure modes and roll out design modifications (such as service bulletins or software updates) to fix them. If corrective actions are successful, the failure rate decreases and the Mean Time Between Failures (MTBF) increases over time. This process is called reliability growth.

The Duane Model (Power Law) James T. Duane discovered that if you plot the cumulative failure rate ($N(t)/t$) against cumulative operating time ($t$) on log-log paper, the data points align along a straight line: ln(N(t) / t) = -α ln(t) + ln(λ) This gives the cumulative failure count equation $N(t) = \lambda t^\beta$, where $\beta = 1 - \alpha$.

Interpreting the Growth Slope (β) The Duane slope parameter $\beta$ classifies reliability growth trends:

• β < 1.0: Positive growth. Failures decrease over time. Modifications are successful.
• β = 1.0: Stable reliability. The instantaneous failure intensity is constant.
• β > 1.0: Deterioration. The failure rate is increasing. System fixes introduce more faults or wear-out is rapid.

Aviation Applications Aviation safety engineers use Duane and Crow-AMSAA models to track flight test safety squawks across accumulated prototype hours. This allows regulatory verification of the mature dispatch reliability target before airworthiness approval is granted.