A note on closure properties of failure rate distributions

Increasing generalized failure rate (IGFR) distributions were introduced as a tool in the study of contracting mechanisms in supply chains. In this note, we compare and contrast the closure – and the lack thereof – of IGFR and increasing failure rate (IFR) distributions with respect to standard operations on random variables. Some implications of these results for the use of IGFR distributions in supply chain models are noted.