Data analysis of progressive‐stress accelerated life tests with group effects

ABSTRACT

Progressive-stress accelerated life testing (PSALT) is a special type of experiment that tests the lifetime of a product with continuously varying stress levels. Due to the limitations of testing equipments and costs, the lifetime data collected by PSALT are usually censored and have group effects. In order to deal with the two characteristics in the data, this paper presents a novel PSALT model with group effects under progressive censoring. Two-stage and Gauss-Hermite quadrature methods are proposed to estimate the model parameters, while the interval estimates are constructed by bootstrap and the asymptotic theorem, respectively. Simulation studies are conducted to compare the proposed model with the traditional models without group effects in terms of the relative bias and root mean squared error under different scenarios. The results show that the proposed model can detect group-to-group variation, and that the models without group effects will result in large biases for estimating the characteristic lifetime of the product. Finally, the proposed model is validated by a real dataset.

KEYWORDS:

• Progressive-stress accelerated life test
• two-stage method
• gauss–hermite quadrature
• progressive censoring

Acknowledgments

The research is supported by Natural Science Foundation of China under grant number 12171432, Zhejiang Xinmiao Talents Program under grant number 2021R429049 and the characteristic & preponderant discipline of key construction universities in Zhejiang province (Zhejiang Gongshang University-Statistics), and Collaborative Innovation Center of Statistical Data Engineering Technology & Application.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work was supported by the Natural Science Foundation of China [12171432]; the characteristic & preponderant discipline of key construction universities in Zhejiang province [Zhejiang Gongshang University-Statistics]; Collaborative Innovation Center of Statistical Data Engineering Technology & Application. [Zhejiang Gongshang University]; Zhejiang Xinmiao Talents Program [2021R429049].

Notes on contributors

Liangliang Zhuang

Liangliang Zhuang is currently pursuing the Ph.D. degree in Statistics with the school of Statistics and Mathematics, Zhejiang Gongshang University. His research interests include degradation modeling and machine learning in reliability engineering.

Ancha Xu

Ancha Xu is a Professor in the School of Statistics and Mathematics at Zhejiang Gongshang University. He received the PhD degree in Statistics from East China Normal University. His current research interests include Bayesian online inference, degradation models, and lifetime data analysis. His articles have appeared in IEEE Transactions on Reliability, Computational Statistics & Data Analysis,Journal of Statistical Planning and Inference, and other technical journals.

Binbing Wang

Binbing Wang is currently pursuing a MS degree in the the School of Statistics and Mathematics at Zhejiang Gongshang University. His main research interests are reliability modeling and Statistical computation.

Yuguo Xue

Yuguo Xue is currently pursuing a MS degree in the the School of Statistics and Mathematics at Zhejiang Gongshang University. His main research interests are reliability modeling and Statistical computation.

Songzi Zhang

Songzi Zhang is currently pursuing a MS degree in the the School of Statistics and Mathematics at Zhejiang Gongshang University. Her main research interests are reliability modeling and Statistical computation.