A doubly accelerated degradation model based on the inverse Gaussian process and its objective Bayesian analysis

References

• McPherson JW. Reliability physics and engineering: time-to-failure modeling. Heidelberg: Springer; 2010.
   Google Scholar
• Whitmore GA. Estimating degradation by a Wiener diffusion process subject to measurement error. Lifetime Data Anal. 1995;1:307–319.
   PubMedGoogle Scholar
• Lim H, Yum BJ. Optimal design of accelerated degradation tests based on Wiener process models. J Appl Stat. 2011;38:309–325.
   Web of Science ®Google Scholar
• Sung SI, Yum BJ. Optimal design of step-stress accelerated degradation tests based on the Wiener degradation process. Qual Technol Quant Manage. 2016;13:367–393.
   Web of Science ®Google Scholar
• Ye ZS, Wang Y, Tsui KL, et al. Degradation data analysis using Wiener processes with measurement errors. IEEE Trans Reliab. 2013;62:772–780.
   Web of Science ®Google Scholar
• Lawless J, Crowder M. Covariates and random effects in a gamma process model with application to degradation and failure. Lifetime Data Anal. 2004;10:213–227.
   PubMed Web of Science ®Google Scholar
• Tseng ST, Balakrishnan N, Tsai CC. Optimal step-stress accelerated degradation test plan for gamma degradation processes. IEEE Trans Reliab. 2009;58:611–618.
   Web of Science ®Google Scholar
• Wang X, Xu DH. An inverse Gaussian process model for degradation data. Technometrics. 2010;52:188–197.
   Web of Science ®Google Scholar
• Ye ZS, Chen N. The inverse Gaussian process as a degradation model. Technometrics. 2014;56:302–311.
   Web of Science ®Google Scholar
• Wang H, Wang GJ, Duan FJ. Planning of step-stress accelerated degradation test based on the inverse Gaussian process. Reliab Eng Syst Safety. 2016;154:97–105.
   Web of Science ®Google Scholar
• Li XY, Hu YQ, Zio E, et al. A Bayesian optimal design for accelerated degradation testing based on the inverse Gaussian process. IEEE Access. 2017;2017:5690–5701.
   Google Scholar
• Duan FJ, Wang GJ. Optimal step-stress accelerated degradation test plans for inverse Gaussian process based on proportional degradation rate model. J Stat Comput Simul. 2017;88:1–24.
   Web of Science ®Google Scholar
• Peng WW, Li YF, Yang YJ, et al. Inverse Gaussian process models for degradation analysis: A Bayesian perspective. Reliab Eng Syst Safety. 2014;130:175–189.
   Web of Science ®Google Scholar
• Peng WW, Li YF, Yang YJ, et al. Bayesian degradation analysis with inverse Gaussian process models under time-varying degradation rates. IEEE Trans Reliab. 2017;66:84–96.
   Web of Science ®Google Scholar
• Berger JO. The case for objective Bayesian analysis. Bayesian Anal. 2006;1:385–402.
   Web of Science ®Google Scholar
• Berger JO, Bernardo JM, Sun DC. The formal definition of reference priors. Ann Statist. 2009;37:905–938.
   Web of Science ®Google Scholar
• Xu AC, Tang YC. Objective Bayesian analysis for linear degradation models. Comm Statist Theory Methods. 2012;41:4034–4046.
   Web of Science ®Google Scholar
• Guan Q, Tang YC, Xu AC. Objective Bayesian analysis accelerated degradation test based on Wiener process models. Appl Math Model. 2016;40:2743–2755.
   Web of Science ®Google Scholar
• He L, He DJ, Cao MX. Objective Bayesian analysis of degradation model with respect to a Wiener process. J Syst Sci Complex. 2016;29:1737–1751.
   Web of Science ®Google Scholar
• He DJ, Tao MZ. Statistical analysis for the doubly accelerated degradation Wiener model: An objective Bayesian approach. Appl Math Model. 2020;77:378–391.
   Web of Science ®Google Scholar
• He DJ, Wang YP, Chang GS. Objective Bayesian analysis for the accelerated degradation model based on the inverse Gaussian process. Appl Math Model. 2018;61:341–350.
   Web of Science ®Google Scholar
• Meeker WQ, Escobar LA. Statistical Methods for Reliability Data. New York: Wiley; 1998.
   Google Scholar
• Peng CY. Inverse Gaussian process with random effects and explanatory variable for degradation data. Technometrics. 2015;57:100–111.
   Web of Science ®Google Scholar
• Jeffreys H. Theory of probability. 3rd ed. Oxford: Oxford University Press; 1961.
   Google Scholar
• Bernardo JM. Reference posterior distributions for Bayesian inference. J R Stat Soc Ser B. 1979;41:113–147.
   Google Scholar
• Berger JO, Bernardo JM. Ordered group reference priors with application to the multinomial problem. Biometrika. 1992;79:25–37.
   Web of Science ®Google Scholar
• Gradshteyn IS, Ryzhik IM. Tables of integrals, series and products. 7th ed. Amsterdam: Elsevier Academic Press; 2007.
   Google Scholar