A generalized Wiener process with dependent degradation rate and volatility and time-varying mean-to-variance ratio

In degradation analysis, there exist two natural features for the degradation data. The first is the dependence of degradation rate and degradation volatility, and the other is the time-varying mean-to-variance ratio. Ignoring them may lead to a significant bias in assessing lifetime information of materials. This paper proposes a generalized Wiener degradation model, which puts these two characteristics and unit-to-unit variation into consideration simultaneously. The proposed model includes many existing Wiener degradation models as special cases. Then, a generalized closed-form approximated residual lifetime distribution is given for the proposed model. Statistical inference for the model parameters is conducted based on the expectation maximizing (EM) method, and two simple auxiliary frameworks are developed for the determination of initial values and the forms of the time-scaled functions. The developed methodologies are then illustrated and verified in a simulation study and two real data analysis.