Statistics and Its Interface

Volume 10 (2017)

Number 3

Optimal progressive Type-I interval censored scheme under step-stress life testing

Pages: 521 – 527



Xuejing Zhao (School of Mathematics & Statistics, Lanzhou University, Lanzhou, China)

Laurent Bordes (Laboratoire de Mathématiques et de leurs Applications, Université de Pau et des Pays de l’Adour, Pau, France)


The parametric estimation and optimal censoring scheme are considered under the progressive multi-stage Type-I censoring scheme as well as step-stress accelerated lifetime model. Nonparametric estimators, using the information of the observable numbers of failures and numbers of censored units at the censoring times, are used to derive estimates of the reliability function at the censoring times. Then two parametric estimators, the maximum likelihood and the minimum-distance, are used to estimate the unknown Euclidean parameters of a parametric model. We use $D$-optimality criterion to determine an optimal sequential step-stress plan under progressive Type-I censoring. Simulation studies are also conducted to assess the finite performance of our estimators.


progressive Type-I interval censoring, cumulative exposure model, Monte-Carlo simulation, step-stress, optimization

2010 Mathematics Subject Classification

Primary 62N01, 62N05. Secondary 65C05.

Published 31 January 2017