Methods employing detergent compositions comprising phosphinosuccinic acid oligomers (PSO) in combination with a sanitizing rinse aid are disclosed. The methods beneficially clean, sanitize and rinse a surface in an efficient two-step process. The detergent compositions employ phosphinosuccinic acid adducts, namely mono-, bis- and oligomeric phosphinosuccinic acid (PSO) derivatives, in combination with an alkalinity source and optionally polymers and/or surfactants. The sanitizing and rinsing compositions employ peroxycarboxylic acid compositions in combination with a nonionic defoaming and wetting surfactant.