The simplified perturbed hard chain theory (SPHCT) equation of state (EOS) possesses several attractive features. We have been exploring possible modifications to the equation to improve its performance for both equilibrium and volumetric property calculations. (In a companion study, we have outlined our strategies for modifying the SPHCT EOS.) As a precursor to our study of modifications to the SPHCT EOS, we (a) developed a robust solution algorithm for the SPHCT, (b) established a novel approach to solving the critical-point constraint equations, and (c) performed a parameter sensitivity analysis study for the equation, each of which is described in the present work, These results provided valuable guidance to our efforts in modifying the SPHCT EOS, which are presented in a companion article. The robust algorithm developed for solution of the SPHCT EOS employs a solution equation written in terms of the compressibility factor. This algorithm exhibits better behavior near both the liquid and vapor roots than previous solution equations. However, this robust behavior requires increased computation time during parameter regressions. The SPHCT parameter sensitivity analysis shows that the characteristic temperature (T*) and the maximum coordination number (Z(M)) have very strong influences on calculated vapor pressures and phase densities. Further, application of the critical constraints yields more stable parameterization than is obtained by utilizing the SPHCT equation in its original form. Simple correlations are presented for solving the critical point constraints. The correlations (a) significantly reduce computational time and complexity and (b) facilitate application of the critical point constraints without the need to embed complicated numerical routines within existing EOS computer codes.