The main purpose of this work is to develop a new multi-way decomposition technique by considering statistical structure of target multi-way array. To this end enhanced multivariance products representation (EMPR), which is an expansion extended from high dimensional model representation (HDMR), is used. EMPR provides quite successful results on representation and approximation of multivariate functions when they have high level multiplicativity. Hence this urges us to reconstruct EMPR as amulti-way array decomposer. This paper presents this decomposition technique with all reconstruction formulations and numerical experiments on synthetic and real-life data sets to denote EMPR's efficiency as a decomposer and also presents a combined method Reductive-EMPR (R-EMPR) as a multi-way array decomposition technique.