Determination of mass, damping coefficient, and stiffness of production system using convolution integral

Discrete event simulation (DES) is most widely used tool for modelling complex production systems. DES model requires skilful mapping of actual production process in a framework used for DES modelling. It also calls for extensive data collection for arriving at probability distributions followed by the time required by various activities involved in production processes and also the probability distribution of various occurrences affecting production process. System dynamics (SD) has also been used to model production system. SD model requires forming causal loop model (stock–flow diagram) showing interrelated influential variables affecting production process, their rates and mathematical relation between cause and effect. Continuous and discrete flow models had also been used for modelling production system. This work proposes a tool for simulating the production output which is simpler as compared to these two techniques. This investigation attempts to establish relationship between inputs to the production system, state of production system and number of units produced. Second-order differential equation analogizing production system with mechanical vibration system is devised and the constants of differential equation are determined. These constants signify mass, damping factor and natural frequency of mechanical vibration system. Differential equation formed for production system helps to simulate the production output in response to forces such as supply order, breakdown and preventive maintenance.