Redundancy in Two-series-parallel and Two-parallel-series Systems with Independent Components Randomly Chosen from Two Batches

In this paper, we study two-series-parallel and two-parallel-series systems with $$\varvec{2n}$$ independent components that are randomly chosen from two different batches. We assume the $$\varvec{n}$$ components from the first batch to be more reliable than those from the second batch with respect to the stochastic order. We then use distortion functions to obtain general results for different redundancy procedures, including the popular active redundancy and minimal repair procedures. The purpose is to determine which batch of components the redundancy should be placed in the system for each subsystem, according to its structure. For a two-parallel-series system, we present some conditions and show that the redundancy mechanism should be assigned to the component from the weaker batch. But, for a two-series-parallel system, under some conditions, we show that the best option is to assign the redundancy to the component from the better batch. Finally, some examples are presented for illustrating all the results established here.