Throughput Evaluation of Buffered Unreliable Production Lines with Machines Having Multiple Failure Modes

Abstract : This paper presents an analytical method to evaluate the system throughput of buffered serial production lines. The machines are unreliable and each machine can have more than one failure and repair modes. The flow of parts through the production line is considered as a continuous flow of material. The proposed method is composed of two main steps. The first one consists of transforming each machine into a single failure and repair mode machine based on a well-known aggregation technique. In the second step, the system throughput is evaluated using an approximate approach called Equivalent Machine Method. This method is based on the analysis of the different states of each buffer using birth-death Markov processes. For each buffer, the birth and death ratios are defined taking into account the probabilities of blockage and starvation of its related upstream and downstream machines. Then, each original machine is defined by its equivalent production rate considering its processing rate, its availability and the influence of the buffers limitations and the other machines. The system throughput is defined as the bottleneck between the equivalent production rates. This method considers both homogeneous and non-homogeneous production lines. A comparative study based on different test instances is presented and discussed. The obtained results prove the effectiveness and the accuracy of the proposed method comparing with both simulation and aggregation methods.