The search for experimental signatures of the critical point (CP) of strongly interacting matter is one of the main objectives of numerous heavy ion collision experiments today. A promising category of CP observables are local fluctuations of the order parameter of the chiral phase transition, which are expected to be scale-invariant, following a universal power-law. An order parameter can be either the chiral $\sigma$-condensate, reconstructed through $\pi^{+}\pi^{-}$ pairs, or the net baryon density $n_B$, and its proxy, the proton density.

Critical fluctuations of the order parameter can be probed through factorial moment intermittency analysis in transverse momentum space. Both dipion and proton intermittency analyses have been performed on NA49 SPS data, providing evidence of critical fluctuations in Si+Si collisions at 158$A$ GeV/$c$. Probes of NA61/SHINE systems either show no intermittency (Be+Be, Pb+Pb), or are inconclusive (Ar+Sc); the analysis is complicated by the presence of large uncertainties, as well as difficulties in handling correlations. We review the current status of intermittency analysis and discuss the challenges involved, such as particle identification and estimating the uncertainties of the intermittency index (power-law exponent $\phi_2$). We propose solutions to these issues through novel statistical techniques and Monte Carlo simulations, presenting their advantages and drawbacks.