Testing an "Exponential Delay Time model'' against a "Random Sign Censoring model'' in Reliability

Résumé

In this paper we consider an industrial system subject to different causes of failure and different types of maintenance: a corrective maintenance is performed after a critical failure and a preventive maintenance can be performed in order to decrease the risk of critical failure. The recurrence of these types of maintenance has been often modeled in a competing risks framework. However rather few statistical inference has been carried out in these models. In particular, there is a need to introduce statistical tests in order to help the engineers to select the model which better fits their data. Thus, in this paper, we introduce a nonparametric test with aim to decide between a Delay Time model with exponential distribution and a Random Sign model. We prove the asymptotic normality of our test statistic and we carry out a Monte Carlo simulation to learn how works our test on finite sample sizes. An application on a real dataset is also given.