Nowadays, systems are more complex and require high reliability for their components, especially critical system components. Therefore, to avoid serious damage, system are often replaced before the actual failure. The replaced parts are considered to have “soft failure”, and the limit in which the parts are replaced is known as the critical level of the degradation process. Determining the appropriate value of the critical level for a product is an important problem in their exploitation, as well as for predicting the Mean Time to Failure (MTTF) or Remaining Useful Lifetime (RUL) of this product based on the degradation data by the mathematical models. In this article, an approach in determining the critical levels based on failure data from an accelerated test is introduced. This approach is applied with the degradation process of Light-Emitting Diodes (LED) in an accelerated test and a type of Wiener process-based model is used to predict the MTTF or RUL of LED based on their degradation data and the found critical level.