Generalization to a Wide Class of Lifetime Distributions

This chapter is the cornerstone of the book.

For any two-parameter lifetime distribution, a nonlinear time transformation is defined, in such a way that, in the transformed time variable, the lifetime probability distribution has an MRL which is a linear function of time.

Then it is possible to apply the properties derived in Chapter 3 to the initial distribution, in particular to derive confidence intervals on the RUL. Important properties of the following failure time distributions are thus obtained: Weibull, Gamma, lognormal; and also to distributions of the first hitting time of a degradation process, such as the Wiener process or the Gamma process.