Computational algorithms for modeling unreliable manufacturing systems based on Markovian property

Performance measure is a critical factor used to judge the effectiveness of a system. In many cases, the ideal performance measure tends to be distorted by failure of machines. Ignoring reliability of equipment when modeling a system will result in overestimation of performance measures. Methods available for modeling unreliable systems involving determination of system-state probabilities are generally difficult and inefficient, especially when limits are set on the buffer size. Based on Markovian property, two computational algorithms are proposed for multi-stage open systems. The objective of these algorithms is to formulate global balance equations for different system states modularly and easily so that system-state probabilities and hence various performance measures can be determined. The elements of a system state are chosen such that they reflect the characteristics of a system as much as possible while keeping the model solution tractable and solvable. Numerical examples are used to illustrate the applications of the proposed algorithms, and their effectiveness and practicability are demonstrated by comparing with results obtained from simulation models.