Abstract
highlights•A new Wiener-process-based reliability estimation approach is developed.•Truncated normal distribution is used to describe the unit-to-unit variability.•The analytical expression of reliability function is derived.•EM algorithm is used to estimate the model parameters effectively.
The use of degradation model to perform the reliability analysis has drawn much attention due to the fact that the performance of numerous highly reliable systems degrades over time. To describe the unit-to-unit variability for a population of systems, the random effect has been incorporated into the degradation model that plays an important part in assessing the reliability of deteriorating systems. In the existing literature, the normal distribution is commonly adopted to represent the random effect, but the assumption can be unsuitable for some practical applications, such as the degradation process of train wheels. In this paper, we present a degradation modeling and reliability estimation approach by using truncated normal distribution to characterize the unit-to-unit variability. A Wiener process with truncated normal distribution is firstly applied to model the degradation process of the deteriorating system, and the analytical expressions of probability density function and reliability function are derived. Expectation maximization algorithm is then used to estimate the model parameters. The effectiveness and feasibility of the presented approach are illustrated through a numerical example and practical case studies for laser devices and train wheels. The results indicate that the presented approach can obtain better reliability estimation results by considering the truncated normal distribution when the unit-to-unit variability has significant difference.