Preservation of the aging intensity order and the preservation of the monotonic aging intensity classes under distorted distributions

This paper presents preservation property of the aging intensity order and the preservation property of the monotonic aging intensity classes under distorted distributions. Several sufficient conditions are given to get the preservation properties. It is shown that the imposed conditions are achievable as we examine in some examples. The preservation of the aging intensity order and the preservation of the decreasing aging intensity class under the structure of a parallel system with independent and identically distributed components' lifetime are made. A lower bound for the aging intensity function of a random lifetime with an increasing failure rate in average distribution is derived. The results are applied to some semiparametric model as a particular standard family of distorted distribution.