IFR (increasing failure rate) : survival function/failure function, 1-F(x), is logconcave.
DFR (decreasing failure rate) : survival function/failure function, 1-F(x), is logconvex.
Failure rate/Hazard rate : h(x)=f(x)/(1-F(x))
Logconcavity :
Logconvexity :
Quasiconcavity and Quasiconvexity:
Source :
http://en.wikipedia.org/wiki/Failure_rate
http://en.wikipedia.org/wiki/Logarithmically_concave_function
http://en.wikipedia.org/wiki/Quasi-concave_function
Shaked and Shanthikumar (2007)