Abstract
Engineering degradation tests allow industry to assess the potential life span of long-life products that do not fail readily under accelerated conditions in life tests. A general statistical model is presented here for performance degradation of an item of equipment. The degradation process in the model is taken to be a Wiener diffusion process with a time scale transformation. The model incorporates Arrhenius extrapolation for high stress testing. The lifetime of an item is defined as the time until performance deteriorates to a specified failure threshold. The model can be used to predict the lifetime of an item or the extent of degradation of an item at a specified future time. Inference methods for the model parameters, based on accelerated degradation test data, are presented. The model and inference methods are illustrated with a case application involving self-regulating heating cables. The paper also discusses a number of practical issues encountered in applications.
Similar content being viewed by others
References
M. Boulanger Carey and R. H. Koenig, “Reliability assessment based on accelerated degradation: A case study,” IEEE Transactions on Reliability vol. 40(5) pp. 499–506, 1991.
R. S. Chhikara and J. L. Folks, The Inverse Gaussian Distribution: Theory, Methodology and Applications, Marcel Dekker: New York, 1989.
D. R. Cox and H. D. Miller. The Theory of Stochastic Processes, Chapman and Hall: London, 1965.
K. A. Doksum and A. Hóyland, “Models for variable-stress accelerated life testing experiments based on Wiener processes and the inverse Gaussian distribution,” Technometrics vol. 34(1) pp. 74–82, 1992.
S. Fook Chong, A Study of Hougaard Distributions, Hougaard Processes and Applications, M.Sc. thesis, McGill University, Montreal, 1993.
R. A. Johnson and D.W. Wichern, Applied Multivariate Statistical Analysis, 3rd edition, Prentice-Hall: Englewood Cliffs, New Jersey, 1992.
M.-L. T. Lee and G. A. Whitmore, “Stochastic processes directed by randomized time,” Journal of Applied Probability vol. 30 pp. 302–314, 1993.
J. Lu, A Reliability Model Based on Degradation and Lifetime Data, Ph.D. thesis, McGill University, Montreal, Canada, 1995.
J. Neter, W. Wasserman and M. H. Kutner, Applied Linear Statistical Models, 3rd edition, Irwin: Homewood, Illinois, 1990.
G. A. Whitmore, “Estimating degradation by a Wiener diffusion process subject to measurement error,” Lifetime Data Analysis vol. 1(3) pp. 307–319, 1995.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Whitmore, G.A., Schenkelberg, F. Modelling Accelerated Degradation Data Using Wiener Diffusion With A Time Scale Transformation. Lifetime Data Anal 3, 27–45 (1997). https://doi.org/10.1023/A:1009664101413
Issue Date:
DOI: https://doi.org/10.1023/A:1009664101413