A new class of Wiener process models for degradation analysis

• We propose a new Wiener process to capture dependence between mean and variance.
• Random-effects Wiener process models are developed so that the variance is increasing in the degradation mean.
• Stress are incorporated into the process in a similar way.
• Statistical inference methods are also developed.
• The methods are applied to two real examples.

For many products, it is not uncommon to see that a unit with a higher degradation rate has a more volatile degradation path. Motivated by this observation, we propose a new class of random effects model for the Wiener process model. We express the Wiener process in a special form and allow one of the parameters to be random across the product population so that a unit with a high degradation rate would also possess high volatility. Statistical inference of the model is discussed. By the same token, we introduce a stress–acceleration relation for the Wiener process so that both the degradation rate and the volatility of the product are increasing in the stress level. The proposed models are demonstrated by analyzing a dataset of fatigue crack growth and a dataset of head wears of hard disk drives. The applications suggest that our models perform better than existing models that ignore the positive correlation between the drift rate and the volatility.