Answer
Shot peening introduces a layer of compressive residual stress on the surface of the wave spring. In high-frequency applications, fatigue cracks almost always initiate at the surface due to tensile stress peaks. The depth of the compressive layer is typically $0.005$ to $0.015$ inches. The total stress $\sigma_{net}$ becomes $\sigma_{applied} - \sigma_{compressive}$. By keeping the net surface stress below the fatigue threshold, shot peening can increase the service life by an order of magnitude. For stainless steels, it also induces a slight work-hardening effect, though care must be taken to avoid 'over-peening' which can cause surface micro-tears in thin cross-section wire ($t < 0.010$ inches).