LSE method using the CHSS model

Pascal Lantieri (1) , Francis Guerin (2) , Sorin Voiculescu (2)

1 LAMPA - PMD - Laboratoire des Arts et Métiers ParisTech d'Angers - Procédés Matériaux Durabilité
2 UA - Université d'Angers

Testing the reliability at a nominal stress level may lead to extensive test time. Estimations of reliability parameters can be obtained faster thanks to step-stress accelerated life tests (ALT). Usually, a transfer functional defined among a given class of parametric functions is required, but Bagdonavičius and Nikulin showed that ALT tests are still possible without any assumption about this functional. When shape and scale parameters of the lifetime distribution change with the stress level, they suggested an ALT method using a model called CHanging Shape and Scale (CHSS). They estimated the lifetime parameters at the nominal stress with maximum likelihood estimation (MLE). However, this method usually requires an initialization of lifetime parameters, which may be difficult when no similar product has been tested before. This paper aims to face this issue by using an iterating least square estimation (LSE) method. It will enable one to initialize the optimization required to carry out the MLE and it will give estimations that can sometimes be better than those given by MLE.

Mots clés: Accelerated life testing; Step-stress test; Weibull distribution; Changing shape and scale; Least square estimation; Bootstrap

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Mécanique des matériaux [physics.class-ph]; Mécanique des matériaux [physics.class-ph]

Pascal Lantieri, Francis Guerin, Sorin Voiculescu. LSE method using the CHSS model. Journal of Statistical Planning and Inference, 2009, 139 (5), pp.1809-1820. ⟨10.1016/j.jspi.2008.05.031⟩. ⟨hal-00881225⟩