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Condition-based maintenance for a degrading system has been attached great importance in reducing unexpected failures and enabling the safe operation of the system. In this paper, we consider a condition-based replacement problem with observed degradation signals for the determination of the optimal replacement time of the system. The observed degradation signals contain some health related information of the system so that the system's health state may be more accurately estimated and the future degradation progression of the system can be predicted. Based on the predicted degradation state, the concerned replacement problem is formulated in the framework of the Markov decision process and then a new degradation-modeling framework based on maximum likelihood estimation is proposed to analyze the degradation signals and to predict the future degradation state of the system. To solve the proposed condition-based replacement decision problem, we analyze structural properties of the optimal replacement policy and an optimal monotonic control limit solution policy is developed for condition-based replacement. Finally, a case study is provided to illustrate the proposed optimal replacement method. [ABSTRACT FROM AUTHOR]

• Box-Cox transformation is introduced in nonlinear degradation modeling. • Transformed degradation data are modeled by wiener process. • Two-stage estimation procedure is presented to identify the model parameters. • Closed-form remaining useful life distribution is derived for prognostics. • The proposed method is validated by degradation data of batteries and LCDs. Transforming nonlinear degradation paths into nearly linear ones has been widely used for nonlinear degradation modeling and prognostics. However, types of the current transformation functions are difficult to determine. This paper addresses issues in nonlinear stochastic degradation modeling and prognostics from a Box-Cox transformation (BCT) perspective. Specifically, the BCT is first used to transform the nonlinear degradation data into nearly linear data, and then the Wiener process with random drift is utilized to model the evolving process of the transformed data. To determine the model parameters, a two-stage estimation procedure is developed including offline stage and online stage. In the offline stage, the parameters are determined via maximum likelihood estimation method based on the historical degradation data and such estimated values are used to initialize the online stage. During the online stage, the Bayesian method is adopted to update the model parameters using the data of the degrading system in service, in which the hyperparameters are updated by the expectation maximization algorithm. A closed-form solution to remaining useful life with updated model parameters is further derived for prognostics. Finally, case studies for lithium-ion batteries and liquid coupling devices are provided to demonstrate the proposed approach. [ABSTRACT FROM AUTHOR]