We present a new method for analyzing X-ray data from clusters of galaxies. The method uses hundreds of X-ray emitting plasma "blobs". Each blob is assigned its own temperature, abundances, position, luminosity, and size. The X-ray data for this complex model is generated by Monte Carlo simulations for both XMM-Newton RGS and EPIC data. Iterations of blob parameters are performed using Markov ... [Show full abstract] chains and a complete set of statistical realizations that are consistent with the observations are obtained. We apply the method to RGS observations of Perseus and M87. This approach demonstrates in a model-independent context the failure of the cooling flow model and places detailed spatially-resolved emission measure constraints on cooling flow models. We also present EPIC results of Abell 1689 using this approach. We expect that these techniques will lead to an easier comparison of X-ray results with those of weak/strong lensing and SZ observations in future studies.