In this study, a semi - Markovian inventory model of type (s, S) is considered and the model is expressed by a modification of a renewal - reward process (X(t)) with an asymmetric triangular distributed interference of chance and delay. The ergodicity of the process X(t) is proved under some weak conditions. Additionally, exact expressions and three - term asymptotic expansions are found for all the moments of the ergodic distribution. Finally, obtained asymptotic results are compared with exact results for a special case.[Hanalioglu, Zulfiye] Karabuk Univ, Dept Actuarial Sci & Risk Management, Karabuk, Turkey; [Khaniyev, Tahir] TOBB Univ Econ & Technol, Dept Ind Engn, TR-06560 Ankara, Turkey