Stochastic models for reliable and unreliable flexible manufacturing cells with two machines and two robots

Manufacturing systems are usually designed in automated units, called cells, and flexibility is introduced so that a variety of parts can be produced on the same set of equipment. In this paper, we consider a Flexible Manufacturing Cell (FMC) consisting of two machines, each served by a robot arm for loading and unloading purposes, and a common pallet handling system, which moves a batch of mixed parts into and out of the system. Two mathematical models are developed to study and compare operations of two cases of the described FMC. In the first case, both machines are assumed to be reliable all the time while in the second case both machines are assumed to be unreliable and subject to unexpected failures. Machining times, robot loading and unloading times, machine failure and repair times and pallet handling times are assumed to be random variables. Stochastic model of each system turns out to be a Markov chain with a transition matrix, whose size depends on the pallet capacity. Case examples are considered for each FMC, exact numerical solutions are obtained, and the production performance results, such as the production rate and equipment utilisations, are compared.