Modelling degradation with multiple accelerated processes

Abstract

Multivariate degradation models are important tools for reliability assessment of highly reliable products. The multivariate aspect of the models depends on the device under study and the type of test applied to it. A device may exhibit different performance characteristics (PC) or one PC may be affected by multiple environmental conditions. If a device is affected by multiple environmental conditions, then it is possible to subject it to multiple accelerating variables in an accelerated degradation test in order to obtain reliability information. In this paper, two accelerating stress variables are considered, which characterize two degradation processes (DP) on a PC. In this way, two degradation models based on the life–stress Arrhenius relationship and the inverse power law relationship are provided. It is shown that the final distribution function characterizing the failure times for each DP can be used to estimate the reliability of a fuel sensor, the example under study in this paper. The interaction of the models with respect to the DPs is described via copula¹ function, in order to model the dependency structure. A Bayesian approach is proposed to estimate the parameters of the final models and the best fit models are selected using information criteria.

Keywords:

• Degradation model
• Accelerated testing
• Bayesian approach
• Arrhenius relationship
• inverse power law

Notes

Acknowledgements

The authors would like to thank the Associate Editor and the anonymous referees for their valuable comments that greatly improved this manuscript. This work was supported by the National Council for Science and Technology of México.

Disclosure statement

The authors report no conflicts of interest. The authors alone are responsible for the content and writing of this article.

Notes on contributors

Luis A. Rodríguez-Picón is currently a PhD student at the Institute of Engineering and Technology at the Autonomous University of Ciudad Juárez, México. He will receive his Ph.D. in Science in Engineering. He received his BS and MS degrees in Industrial Engineering from the Technological Institute of Ciudad Juárez, México, in 2010 and 2012, respectively. He has worked as a professor in the area of statistics and mathematics and has professional experience in the automotive industry. His research interests includes reliability modelling, Bayesian inference, stochastic modelling and statistical quality control.

Manuel I. Rodríguez Borbón is a Professor at the Institute of Engineering and Technology at the Autonomous University of Ciudad Juárez, México. He received his PhD in Industrial Engineering from the New Mexico State University, USA. He holds a M.S. in Statistics from the University of Texas at El Paso, USA, and a B.S. in industrial engineering from the Technological Institute of Ciudad Juárez, México. His research interest includes reliability data analysis, accelerated testing, maintainability and statistical computing.

Delia Valles-Rosales is an Associate Professor in the Department of Industrial Engineering at New Mexico State University. Delia is originally from México. She received her BS from the Instituto Tecnológico de Durango and PhD from New Mexico State University. Her research uses nature to inspire the development of innovative manufacturing processes, new processes of biomass utilization in the plastic industry, and models and algorithms for system optimization in agriculture, industry, and service areas. Dr. Valles-Rosales is currently a NMSU Director of the BGREEN (Building Regional Energy and Educational Alliances) Program funded by USDA.

Victor H. Flores Ochoa is a PhD student at the Technological Institute of Ciudad Juárez, México. He received his BS and MS degrees in industrial engineering from the Technological Institute of Ciudad Juárez, México. He has several years of experience on the automotive industry, and has occupied managerial and director positions. His research interest includes uncertainty in measurement systems, statistical quality control and reliability engineering.

Notes

1 Copulas are functions that join univariate distribution functions to build multivariate distributions, thus, is a function defined in [0,1]² with uniform marginal distributions [0, 1].

2 *

3 , where L is the maximized value of the likelihood function for the estimated model, k is the number of free parameters to be estimated and n is the number of data points.