The highly accelerated stress test (HAST) method was first proposed by Jeffrey E. Gunn, Sushil K. Malik, and Purabi M. Mazumdar of IBM. The acceleration factor for elevated humidity is empirically derived to be
A F H = e const ⋅ ( R H s n − R H o n ) , {\displaystyle AF_{\text{H}}=e^{{\text{const}}\cdot (RH_{\text{s}}^{n}-RH_{\text{o}}^{n})},}
const {\displaystyle {\text{const}}} is a value which normally goes from 0.1 to 0.15 where RHs is the stressed humidity, RHo is the operating-environment humidity, and n is an empirically derived constant (usually 1 < n < 5). The acceleration factor for elevated temperature is derived to be
A F T = e ( E a / k ) ( 1 / T o − 1 / T s ) , {\displaystyle AF_{T}=e^{(E_{\text{a}}/k)(1/T_{\text{o}}-1/T_{\text{s}})},}
where Ea is the activation energy for the temperature-induced failure (most often 0.7 eV for electronics), k is the Boltzmann constant, To is the operating temperature in kelvins, and Ts is the stressed temperature. Therefore the total acceleration factor for unbiased HAST testing is
A F HAST = A F H ⋅ A F T = e const ⋅ ( R H s n − R H o n ) e ( E a / k ) ( 1 / T o − 1 / T s ) . {\displaystyle AF_{\text{HAST}}=AF_{\text{H}}\cdot AF_{T}=e^{{\text{const}}\cdot (RH_{\text{s}}^{n}-RH_{\text{o}}^{n})}e^{(E_{\text{a}}/k)(1/T_{\text{o}}-1/T_{\text{s}})}.}
See also Highly accelerated life test (HALT) – Stress testing methodology for enhancing product reliability Reliability engineering § Accelerated testing Accelerated life testing – Process of testing a product Fault injection
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