The purpose of this paper is to introduce some properties of generalized failure rate (GFR) and generalized reversed failure rate (GRFR), study their connection with inequality measures and then apply it to make comparisons of some reliability models. In the second part of our paper, we obtain the properties for the GRFR based on the properties of the GFR and weighted distributions. The importance of such a study lies in the usefulness of using. Finally, we present two examples to illustrate the applications of the relationships outlined in this paper. A real dataset is used for clarifying presented concepts.
One of the principal subjects in multiple criteria decision analysis is ranking alternatives. Here, we present a new method to rank alternatives by using data envelopment analysis. In this paper, one ranking method is proposed based on applying an artificial alternative called aggregate alternative. The method is based on the fact that one efficient alternative with a better performance has stronger effects on the group of other alternatives. That means its deletion forces the remaining alternatives to get smaller efficiency. The described idea in this paper is inspired of Lotfi and et al. (2011). One feature of the proposed method is that it does not need to determine the weight of the prior. Two examples are used to illustrate how the proposed method works in actual practices, and the results are compared with those obtained from the TOPSIS method.
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