Early detection of change-point in hazard rate with small sample size

Laurent Bordes (1) , Frédéric Ibled (2) , Christian Paroissin (1) , Jean-Christophe Turlot (1)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 Alstom Transport - Alstom Transport

In this paper we address the problem of deciding if either $n$ consecutive independent failure times have the same failure rate or if there exists some $k\in\{1,\ldots,n\}$ such that the common failure rate of the first $k$ failure times is different from the common failure rate of the last $n-k$ failure times. The statistical tests we propose are based on mean ratio under the assumption that lifetimes are exponentially distributed and on Mann-Whitney or precedence test statistics when no parametric assumption on the underlying distribution is done. Our statistics are free of the unknown underlying distribution under the null hypothesis of homogeneity of the $n$ failure times which allows to compute critical values of our tests by Monte Carlo methods for small sample size. These tests have been developed in order to perform sequential change-point analysis of small sets of feedback data. They are applied to feedback data from Alstom Transport in order to detect an early change-point of the failure rate of an industrial equipment.

Mots clés: Change-point; Hazard rate; Exponential distribution; Mann-Whitney test; Precedence test; Statistical tables

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Méthodologie [stat.ME]; Applications [stat.AP]

Laurent Bordes, Frédéric Ibled, Christian Paroissin, Jean-Christophe Turlot. Early detection of change-point in hazard rate with small sample size. 2010. ⟨hal-00507452v2⟩