Mixtures of reliability functions and failure rates are frequently used as tools to model data on lifetimes of heterogeneous items. Which type of these mixtures to use, however, is an unsettled question. We introduce a more flexible mixture model, referred to as the alphamixture, which gives
the reliability and failure rate mixtures as special cases, as well as providing various degrees of compromise between the two conventional mixtures and much more beyond the two wellknown types. The mixture inherits stochastic order from properties of the weighted power mean. We establish a benchmark for the compromise between mixtures of two failure rates and two reliability functions based on the notion of stochastic distance between distributions. Several results on the failure rate properties of the mixture are given and illustrated through examples of mixtures of wellknown reliability models. This new reliability model provides a flexible tool for modeling lifetime of heterogeneous items and the results provide useful insight for theoreticians.
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