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For some reliability systems, it is possible to have the system reliability smaller than the reliability obtained using the configuration of the components. This may be due to the inefficiency of the system. By inefficiency, we mean any tendency or attribute that will bring down the performance of the system from the level the configuration is capable of or expected to provide or designed for. This sets a maximum limit (or frontier) for the performance of the system. Therefore, deviation of the observed level from this limit would then be an indicator of the inefficiency. In this paper, we have made an attempt to model inefficiencies in the working of a reliability system, and to define an inefficiency index. The paper discusses the practical estimation of the coefficient of inefficiency in the system performance. The stochastic frontier regression methods are used to estimate the inefficiency. The validity of the methodology has been assessed for an exponential model, using a limited simulation study. The inefficiency indices proposed in this paper are simple, as they must be to be useful to engineers. We found that the suggested indices & their estimation procedures work well.