There has been growing interest in study of reliability function such as reversed failure rate and its properties and applications. Some of them are similar to those of failure rate and some have different approach and motivation. Distribution with an increasing (decreasing) generalized failure rate IGFR (DGFR) has useful applications in pricing and supply chain problems. Many distributions with their GFR and the closure properties of them have important role in economical aspects. Some notion of ageing is related to generalized reversed failure rate with the implications and view to the link with elasticity function is obtained and mentioned shortly. The DGRFR and related version are studied via a variant point of view criteria and also discussed closure properties. The weighted distributions with monotone generalized reversed failure rate is our concentration for finding more approach and result based on the GRFR of original distribution whichis the last part of the paper.

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