Step-stress tests for interval-censored data under gamma lifetime distribution

Abstract

Inferential methods under extreme form of censoring are of interest in reliability theory because of their applicability to practical engineering problems. interval-censored data naturally appear in many situations wherein the exact failure times cannot be observed, but we can only know if the product has failed before a certain inspection time or not. In addition, some products are highly reliable with large mean lifetimes under normal operating conditions, and so accelerated lifetime tests (ALTs) need to be carried out for inferential purposes. Step-stress ALTs increase such stress factors at certain pre-fixed times, thus inducing early failure. Likelihood-based estimation methods are known to have a very good performance in the absence of contamination in the data, but they perform poorly when few observations do not follow the same distribution as the rest of the observations. In this work, we develop robust estimators and Wald-type test statistics based on density power divergence (DPD) method under step-stress ALT model and gamma lifetime distribution based on interval-censored test data. The performance of the proposed estimators and test statistics are then empirically examined through an extensive simulation study. Finally, the usefulness of the developed inferential methods is illustrated with a real kinetics data.

Keywords:

• Accelerated life tests
• density power divergence
• gamma distribution
• one-shot devices
• robustness

Additional information

Funding

This work was supported by Ministry of Education and Vocational Training of Spain; Natural Sciences and Engineering Research Council of Canada; Ministry of Universities of Spain.

Notes on contributors

Narayanaswamy Balakrishnan

Narayanaswamy Balakrishnan received his BSc and MSc degrees in Statistics from the University of Madras, India, in 1976 and 1978, respectively. He finished his PhD in Statistics from the Indian Institute of Technology, Kanpur, India, in 1981. He is a Distinguished University Professor at McMaster University, Hamilton, ON, Canada. His research interests include distribution theory, ordered data analysis, censoring methodology, reliability, survival analysis, non-parametric inference, and statistical quality control. Prof. Balakrishnan is a Fellow of the American Statistical Association and a Fellow of the Institute of Mathematical Statistics. He is currently the Editor- in-Chief of Communications in Statistics.

María Jaenada

María Jaenada is an Assistant Professor in the Department of Statistics and Operational Research, Complutense University of Madrid (Spain). She received the B.Sc. degree in mathematics and in statistics and the M.Sc. degree in computational statistics from the Universidad Complutense de Madrid, where she is currently pursuing the Ph.D. degree in mathematical engineering, statistics, and operations research with the Department of Statistics and Operational Research, under the supervision of Prof. Leandro Pardo. Her research interests include reliability analysis and robust inferential methods.

Leandro Pardo

Leandro Pardo received the B.Sc. and Ph.D. degrees in mathematics from the Complutense University of Madrid, Spain, in 1976 and 1980, respectively. He has been a Full Professor with the Department of Statistics and Operational Research, Faculty of Mathematics, Complutense University of Madrid, since 1993. He was elected as a Distinguished Eugene Lukacs Professor with Booling Green University, Booling Green, Ohio, in 2004. He was the President of the Spanish Society of Statistics and Operations Research (SEIO) from 2013 to 2016. He was an Editor-in-Chief of TEST from 2005 to 2008.