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Paper   IPM / M / 15814
School of Mathematics
  Title:   The alpha-mixture of survival functions
  Author(s):  Majid Asadi (Joint with N. Ebrahimi aand E. S. Soofi)
  Status:   Publishied
  Journal: J. Appl. Probab.
  Vol.:  56
  Year:  2019
  Pages:   1151-1167
  Supported by:  IPM
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 alpha-mixture, 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 well-known 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 well-known 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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