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This paper deals with modeling steady-state behavior of a single-product, pull-type, serial supply chain, frequently encountered in the automotive industries. The proposed analytical method enables projection of the end-customer demand information to upstream of the supply chain and estimate demand forecast at the individual tier levels. The supply chain performance assessment is based on the Due-Time Performance metric (DTP - probability to ship a required product/parts volume in a fixed time interval) under the assumption of customer demand following a discrete time Markov process, a special case for correlated demands. A numerical case study demonstrates the use of the DTP measure for a two-tier supply chain. The analytical results (verified by simulations) quantify important relationships in the supply chain, involving reliabilities of machines/stations, capacities of the buffers, demands correlation, and the due times and will find use in performance assessment, optimization and design of supply chains.