A Generalized Wiener Process Degradation Model with Two Transformed Time Scales

Degradation analysis is very useful in reliability assessment for complex systems and highly reliable products, because few or even no failures are expected in a reasonable life test span for them. In order to further our study on degradation analysis, a novel Wiener process degradation model subject to measurement errors is proposed. Two transformed time scales are involved to depict the statistical property evolution over time. A situation where one transformed time scale illustrates a linear form for the degradation trend and the other transformed time scale shows a generalized quadratic form for the degradation variance is discussed particularly. A one-stage maximum likelihood estimation of parameters is constructed. The statistical inferences of this model are further discussed. The proposed method is illustrated and verified in a comprehensive simulation study and two real applications for indium tin oxide (ITO) conductive film and light emitting diode (LED). The Wiener process model with mixed effects is considered as a reference. Comparisons show that the proposed method is more general and flexible, and can provide reasonable results, even in considerably small sample size circumstance.