Stochastic comparisons between used redundant systems andredundant systems with used components

One of the important aims in reliability engineering is to improve the performance and increasethe reliability of systems. Increasing the reliability of a system is possible by allocating redundancies components in the structure of the system. In this paper, we use the worked and functioning spares components in the structure of coherent systems to increase its performance. The stochastic comparisons between used redundant coherent systems and redundant coherent systems with used components done. A comparison of used redundant systems and redundant system with used components will the design engineers to build more reliable system out of the good components of a failed system. Using the distortion function, we obtain a mixture representation for the lifetime of the mentioned systems. Based on different random stochastic orders, we provide conditions on reliability functions that used redundant coherent systems work better (worse) than redundant coherent systems with used components.