Template-Type: ReDIF-Paper 1.0
Author-Name: Frenk, J.B.G.
Author-Name-Last: Frenk
Author-Name-First: Hans
Author-Name: Nicolai, R.P.
Author-Name-Last: Nicolai
Author-Name-First: Robin
Author-Person: pni60
Title: Approximating the Randomized Hitting Time Distribution of a Non-stationary Gamma Process
Abstract: The non-stationary gamma process is a non-decreasing stochastic process with independent increments. By this monotonic behavior this stochastic process serves as a natural candidate for modelling time-dependent phenomena such as degradation. In condition-based maintenance the first time such a process exceeds a random threshold is used as a model for the lifetime of a device or for the random time between two successive imperfect maintenance actions. Therefore there is a need to investigate in detail the cumulative distribution function (cdf) of this so-called randomized hitting time. We first relate the cdf of the (randomized) hitting time of a non-stationary gamma process to the cdf of a related hitting time of a stationary gamma process. Even for a stationary gamma process this cdf has in general no elementary formula and its evaluation is time-consuming. Hence two approximations are proposed in this paper and both have a clear probabilistic interpretation. Numerical experiments show that these approximations are easy to evaluate and their accuracy depends on the scale parameter of the non-stationary gamma process. Finally, we also consider some special cases of randomized hitting times for which it is possible to give an elementary formula for its cdf.
Creation-Date: 2007-05-24
File-URL: https://repub.eur.nl/pub/10149/ERS-2007-031-LIS.pdf
File-Format: application/pdf
Series: RePEc:ems:eureri
Number: ERS-2007-031-LIS
Classification-JEL: C53, M, M11, O31, O32, O33
Keywords: Approximation, Condition based maintenance, First hitting time, Non-stationary gamma process, Random threshold
Handle: RePEc:ems:eureri:10149