Mis-specification analysis of Wiener degradation models by using f-divergence with outliers

• Published in: Reliability engineering & system safety Vol. 195; p. 106751
• Main Authors: Zhang, Fode, Ng, Hon Keung Tony, Shi, Yimin
• Format: Journal Article
• Language: English
• Published: Barking Elsevier Ltd 01.03.2020; Elsevier BV
• Subjects: Computer simulation; Contaminated data; Contamination; Data analysis; Datasets; Degradation; Degradation model; Differential geometry; f-Divergence; Geometry; Mathematical models; Mis-specification analysis; Outliers (statistics); Parameter estimation; Parameter robustness; Reliability analysis; Reliability engineering; Robust estimation; Robustness (mathematics); Specifications; Statistical analysis; Statistical models; f-Divergence; Robust estimation; Mis-specification analysis; Contaminated data; Degradation model
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2019.106751

•The mis-specification analysis of the degradation model is studied.•The minimum f-divergence estimation is discussed.•The estimation method is illustrated by using Kullback-Leibler divergence.•The unit-level and measurement-level contamination data are considered.•The simulation results and the real data analysis are reported. Degradation models have been investigated extensively for the evaluation of the quality and reliability of highly reliable products. In practical applications, the proper model of a degradation dataset is often unknown and misspecified for one thing; the dataset may be contaminated or contains outliers for another. Here, contamination means the degradation measurements are inspected embedded by noise with different levels. Thus, it is necessary to discuss the model mis-specification analysis and degradation data analysis when the degradation measurements contain outliers. Information geometry is a theory of using modern differential geometry to investigate the structure of manifolds induced by the statistical models, and the f-divergence is a popular tool in information geometry. This paper focuses on the model mis-specification analysis by employing the f-divergence as a tool to measure the difference between the true model and suggested models. A robust parameter estimation method based on minimizing the f-divergence is proposed. The results based on Kullback–Leibler divergence are obtained as an illustration. Simulation results and two numerical examples are used to illustrate the advantages of the proposed methodologies.