We establish here an integral inequality for real log-concave functions, which can be viewed as an average monotone likelihood property. This inequality is then applied to examine the monotonicity of failure rates.

中文翻译：

---

对数凹函数不等式及其在故障率研究中的应用

我们在这里建立实对数凹函数的积分不等式，它可以被视为平均单调似然属性。然后应用这个不等式来检查故障率的单调性。