Optimal step-stress accelerated degradation test plans for inverse Gaussian process based on proportional degradation rate model

ABSTRACT The purpose of this paper is to address the optimal design of the step-stress accelerated degradation test (SSADT) issue when the degradation process of a product follows the inverse Gaussian (IG) process. For this design problem, an important task is to construct a link model to connect the degradation magnitudes at different stress levels. In this paper, a proportional degradation rate model is proposed to link the degradation paths of the SSADT with stress levels, in which the average degradation rate is proportional to an exponential function of the stress level. Two optimization problems about the asymptotic variances of the lifetime characteristics' estimators are investigated. The optimal settings including sample size, measurement frequency and the number of measurements for each stress level are determined by minimizing the two objective functions within a given budget constraint. As an example, the sliding metal wear data are used to illustrate the proposed model.

[1]  Weiwen Peng,et al.  Bivariate Analysis of Incomplete Degradation Observations Based on Inverse Gaussian Processes and Copulas , 2016, IEEE Transactions on Reliability.

[2]  Heonsang Lim.  Optimum Accelerated Degradation Tests for the Gamma Degradation Process Case under the Constraint of Total Cost , 2015, Entropy.

[3]  Zhengqiang Pan,et al.  Optimal Design for Step-Stress Accelerated Degradation Test with Multiple Performance Characteristics Based on Gamma Processes , 2014, Commun. Stat. Simul. Comput..

[4]  William Q. Meeker,et al.  Accelerated Destructive Degradation Test Planning , 2009, Technometrics.

[5]  K. Doksum,et al.  Models for Variable-Stress Accelerated Life Testing Experiments Based on Wiener Processes and the Inverse Gaussian Distribution , 1992 .

[6]  Weiwen Peng,et al.  A Bayesian optimal design for degradation tests based on the inverse Gaussian process , 2014 .

[7]  Hao Qin,et al.  Inverse Gaussian process-based corrosion growth model for energy pipelines considering the sizing error in inspection data , 2013 .

[8]  Weiwen Peng,et al.  Inverse Gaussian process models for degradation analysis: A Bayesian perspective , 2014, Reliab. Eng. Syst. Saf..

[9]  N. Balakrishnan,et al.  Bivariate degradation analysis of products based on Wiener processes and copulas , 2013 .

[10]  Zhengqiang Pan,et al.  Bivariate Constant-Stress Accelerated Degradation Model and Inference , 2011, Commun. Stat. Simul. Comput..

[11]  W. Meeker.  Accelerated Testing: Statistical Models, Test Plans, and Data Analyses , 1991 .

[12]  Zhengqiang Pan,et al.  Reliability modeling of degradation of products with multiple performance characteristics based on gamma processes , 2011, Reliab. Eng. Syst. Saf..

[13]  Jen Tang,et al.  Optimum step-stress accelerated degradation test for Wiener degradation process under constraints , 2015, Eur. J. Oper. Res..

[14]  J. Bert Keats,et al.  Statistical Methods for Reliability Data , 1999 .

[15]  W. R. Schucany,et al.  Generating Random Variates Using Transformations with Multiple Roots , 1976 .

[16]  Narayanaswamy Balakrishnan,et al.  Optimal Step-Stress Accelerated Degradation Test Plan for Gamma Degradation Processes , 2009, IEEE Transactions on Reliability.

[17]  Chien-Yu Peng,et al.  Inverse Gaussian Processes With Random Effects and Explanatory Variables for Degradation Data , 2015, Technometrics.

[18]  W. Nelson.  Statistical Methods for Reliability Data , 1998 .

[19]  Xiao Wang,et al.  An Inverse Gaussian Process Model for Degradation Data , 2010, Technometrics.

[20]  Ewan Macarthur,et al.  Accelerated Testing: Statistical Models, Test Plans, and Data Analysis , 1990 .

[21]  Luis A. Escobar,et al.  Accelerated degradation tests: modeling and analysis , 1998 .

[22]  Huan Wang,et al.  Planning of step-stress accelerated degradation test based on the inverse Gaussian process , 2016, Reliab. Eng. Syst. Saf..

[23]  Loon Ching Tang,et al.  Accelerated Degradation Test Planning Using the Inverse Gaussian Process , 2014, IEEE Transactions on Reliability.

[24]  Bong-Jin Yum,et al.  OPTIMAL DESIGN OF ACCELERATED DEGRADATION TESTS FOR ESTIMATING MEAN LIFETIME AT THE USE CONDITION , 1997 .

[25]  Weiwen Peng,et al.  Reliability of complex systems under dynamic conditions: A Bayesian multivariate degradation perspective , 2016, Reliab. Eng. Syst. Saf..

[26]  M. Boulanger,et al.  Experimental Design for a Class of Accelerated Degradation Tests , 1994 .

[27]  Zhengqiang Pan,et al.  Residual life estimation under time-varying conditions based on a Wiener process , 2017 .

[28]  B. Guo,et al.  Residual life estimation based on bivariate Wiener degradation process with time-scale transformations , 2014 .

[29]  N. Balakrishnan,et al.  Residual life estimation based on bivariate non-stationary gamma degradation process , 2015 .

[30]  Weiwen Peng,et al.  Bayesian Degradation Analysis With Inverse Gaussian Process Models Under Time-Varying Degradation Rates , 2017, IEEE Transactions on Reliability.

[31]  D.,et al.  Regression Models and Life-Tables , 2022 .

[32]  Hao Zhang,et al.  Design of PH-based accelerated life testing plans under multiple-stress-type , 2007, Reliab. Eng. Syst. Saf..

[33]  Sheng-Tsaing Tseng,et al.  Optimal design for step-stress accelerated degradation tests , 2006, IEEE Trans. Reliab..

[34]  Nan Chen,et al.  The Inverse Gaussian Process as a Degradation Model , 2014, Technometrics.

[35]  Naijun Sha,et al.  Bayesian analysis for step-stress accelerated life testing using weibull proportional hazard model , 2014 .