A manufacturing system is governed by its various processes upon which its efficiency is dependent. Since, failure results in considerable losses, many manufacturing systems have certain redundancies for some processes. These redundancies cause the system to work under different efficiency states called multi-state elements. In this paper various processes of metal sheet manufacturing unit have been categorized as subsystems to determine the multi-state probabilities of its different efficiency states. Artificial Neural Network Technique (ANN) has been used to estimate the change in these multi-state probabilities over time. The ANN has also been used to estimate variation in upstate and downstate probabilities of the system for a particular-time period. The results have been used to determine variation in profit over time for the system.