Optimizing a charged particle optical system utilizing a high brightness source requires the inclusion of the effect of Coulomb interactions in the evaluations. A new computer program package, named ANALIC, has bean developed to perform the combined calculation of lens aberrations, space charge aberrations, and statistical Coulomb effects in a complete instrument. By making use of an analytical slice method, valid for weak/incomplete collisions, to calculate the Coulomb interactions, the program combines reasonable accuracy with high speed. Using ANALIC, an optical system with an arbitrary number of lenses and apertures, an arbitrary mode of imaging, and an arbitrary distribution of the beam energy can be analyzed directly. The functions, features, organization, and calculation approach of the program are reported. As an example of the use of the program, a four lens electron probe instrument is analyzed for the demonstration of the combined calculation and optimization process of a particle optical system.