Bayesian analysis of accelerated life test under constrained randomization

Abstract

Reliability engineers typically prioritize the lower percentiles. Accurately assessing these lower percentiles enables engineers to delve deeper into early product failures, paving the way for enhanced product reliability. In the manufacturing realm, many accelerated life tests (ALTs) veer away from completely randomized designs (CRDs) due to constraints in time and budget. Within ALTs, alterations in stress can lead to shifts in the failure mechanism of products. To accurately discern product lifetime percentiles, there is an imperative need to account for these varying failure mechanisms and random effects. Our approach introduces a re-parameterization model encapsulating random effects and disparate failure mechanisms. In this model, a specific percentile is employed as a stand-in for the scale parameter, laying the groundwork for a regression model interlinking the percentile, acceleration stress, and random effect. Concurrently, a separate regression model is designed for shape parameters in relation to acceleration stresses. Leveraging the Bayesian method, we ascertain the estimated values for the model parameters. The model is applied to an ALT example focusing on glass capacitors. The simulations underline the model’s prowess in delivering a more precise estimation of lower lifetime percentiles. Additionally, the Bayesian method further refines the accuracy of the lifetime percentile estimations.

Keywords:

• Accelerated life test
• re-parameterization model
• random effects
• nonconstant shape parameters
• Weibull distribution

Additional information

Funding

This work was supported by the National Natural Science Foundation of China under Grants [numbers 72002066, 71871204, and 71902138]; the Humanity and Social Science Youth Foundation of Ministry of Education of China under Grant [number 19YJC630181].

Notes on contributors

Shanshan Lv

Guodong Wang is an associate professor in the Department of management engineering at Zhengzhou University of Aeronautics, Zhengzhou, China. He received his BS Applied Mathematics from Nanchang University of Aeronautics, Nanchang, China, an MS degree in Reliability Engineering from Beihang University, Beijing, China, and a PhD in Quality Engineering from Tianjin University, Tianjin, China. His research interests focus on design of experiments and reliability improvement.

Fan Li

Shanshan Lv is a lecturer in the School of Economics and Management at Hebei University of Technology. She received her B.S. degree from Zhengzhou University in 2012, M.S. and Ph.D. degree from Tianjin University, Tianjin, China, 2018, respectively. Her research interests include design of experiments, reliability analysis and improvement, and multi-response optimization.

Guodong Wang

Fan Li received the B.S. degree in economics from Hebei University of Science and Technology in 2020. She is currently a master degree candidate in the School of Economics and Management at the Hebei University of Technology, Tianjin. Her fields of interest are quality engineering and quality management.

Sen Li

Sen Li received the B.S. degree in Industrial Engineering from the Zhengzhou University of Aeronautics, Zhengzhou, in 2020. He is currently a master degree candidate in the School of Economics and Management at the Hebei University of Technology, Tianjin. His fields of interest are reliability engineering, quality control and management.