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This paper considers a production problem for a transfer line subject to random failures and repairs, and differs from other studies on transfer lines. It considers a manufacturing system consisting of three machines (two machines with passive redundancy, and one in series with the previous ones) producing one part type. The control problem is subject to non-negative constraints on work-in-process (WIP). The decision variables are the production rates of two main machines and a standby machine, and influence the WIP levels, the inventory levels and the system's capacity, which is assumed to be described by a finite-state Markov chain. The objective of this paper is to minimise WIP and finished goods inventory costs; it also aims to respect the essential space–time during intervention on machine down, in order to minimise the possibility of the circumvention of protection devices or of the retraction of lockout/tagout procedures through a passive redundancy system. This paper therefore verifies the effect of passive redundancy on optimal stock levels. Given that an analytical or even a numerical solution of the problem is very difficult to find, and that we want to have a more realistic model for industries, we present a combined approach, which is presented based on a combination of analytical formalism, simulation modelling, design of experiments, and response surface methodology to optimise a transfer line with passive redundancy, producing one part type. The usefulness of the proposed approach is illustrated through a numerical example and a sensitivity analysis. [ABSTRACT FROM PUBLISHER]