Mixture models in profust reliability theory

Conventional (i.e. probist) reliability theory is based on the probability assumption and the binary-state assumption, whereas profust reliability theory is based on the probability assumption and the fuzzy-state assumption. The mixture model is an important form of typical systems in profust reliability theory. In this paper we show that a mixture model can be converted into a series system, and study the IFR and DFR preservabilities for mixture models. Various profust reliability bounds are given for the mixture model. In addition, we also show how to construct typical profust lifetime distributions for mixture models.