Plot alternating stress against life on log-log paper and the S-N curve becomes a straight line. Basquin wrote it down: $\sigma_a = \sigma_f'\,(2N_f)^{b}$ — sigma-a equals sigma-f-prime times two N-f, to the b. $\sigma_a$ is the alternating amplitude in MPa, $\sigma_f'$ the fatigue strength coefficient in MPa (roughly the true fracture strength — the amplitude at a single reversal), $N_f$ the cycles to failure, and $b$ the fatigue strength exponent, a small NEGATIVE number, typically −0.05 to −0.12. Note the 2: fatigue is counted in reversals, and one cycle is two of them, up and back. Forgetting it is the standing error on this equation.

Real loading is not one amplitude, it is a spectrum, and Palmgren and Miner supply the bookkeeping: $D = \dfrac{n_1}{N_1} + \dfrac{n_2}{N_2} + \dfrac{n_3}{N_3}$. Mind the case, because it carries the whole meaning: lowercase $n_i$ is what happened — the cycles actually applied in block $i$ — and capital $N_i$ is what was allowed, the life the S-N curve permits at that block's amplitude. The subscripts 1, 2, 3 simply number the blocks; they are not an order in time. $D$ is the accumulated damage fraction, a bare number, and failure is predicted when it reaches 1.

Each term is a fraction of ONE life. That is why a block with few cycles against a short permitted life can eat more of the structure than a block with ten times the count against a long one — and why rainflow counting a season of strain-gauge data is worth the trouble. Miner's rule is linear, cheerfully ignores the ORDER of the blocks, and real structures sometimes fail at $D$ near 0.5 or survive past 2. Use it, and keep a healthy respect for its scatter.