Degradation data analysis based on a generalized Wiener process subject to measurement error

• Published in: Mechanical systems and signal processing Vol. 94; pp. 57 - 72
• Main Authors: Li, Junxing, Wang, Zhihua, Zhang, Yongbo, Fu, Huimin, Liu, Chengrui, Krishnaswamy, Sridhar
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Ltd 15.09.2017; Elsevier BV
• Subjects: Computer simulation; Correlation analysis; Data analysis; Degradation; Degradation analysis; Distribution functions; Error analysis; Maximum likelihood estimation; Measurement errors; Parameter estimation; Performance degradation; Probability distribution; Probability distribution functions; Resistors; Time correlation functions; Wear; Wiener process; Measurement errors; Maximum likelihood estimation; Wiener process; Degradation analysis
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2017.02.031

[Display omitted] •A generalized Wiener process degradation model with measurement errors is proposed.•A simple method to determine the transformed time scale forms is presented.•The probability distribution function is derived based on the first hitting time.•Maximum likelihood estimation method is used to estimate the unknown parameters.•Simulation and real examples are used to illustrate the efficiency of the model. Wiener processes have received considerable attention in degradation modeling over the last two decades. In this paper, we propose a generalized Wiener process degradation model that takes unit-to-unit variation, time-correlated structure and measurement error into considerations simultaneously. The constructed methodology subsumes a series of models studied in the literature as limiting cases. A simple method is given to determine the transformed time scale forms of the Wiener process degradation model. Then model parameters can be estimated based on a maximum likelihood estimation (MLE) method. The cumulative distribution function (CDF) and the probability distribution function (PDF) of the Wiener process with measurement errors are given based on the concept of the first hitting time (FHT). The percentiles of performance degradation (PD) and failure time distribution (FTD) are also obtained. Finally, a comprehensive simulation study is accomplished to demonstrate the necessity of incorporating measurement errors in the degradation model and the efficiency of the proposed model. Two illustrative real applications involving the degradation of carbon-film resistors and the wear of sliding metal are given. The comparative results show that the constructed approach can derive a reasonable result and an enhanced inference precision.