A series of identities of correlation functions K(n1, n2, …, nN) are given in the nearest-particle system. The above correlation identities are applied to the one-dimensional contact process. The decoupling induced by a renewal measure yields the first approximation: [Formula: see text] for the critical value and [Formula: see text] for the order parameter, which makes a rigorous bound as proved by Holley and Liggett. Furthermore, introducing a new decoupling procedure, improved estimations of [Formula: see text] and [Formula: see text] are calculated.