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Very recently, a new age and state-dependent degradation process, named the Transformed Wiener (TW) process, has been proposed to describe degradation phenomena when the degradation growth of the units under study is not necessarily monotonically increasing and depends stochastically on the current degradation level. This paper suggests a Bayesian estimation approach for such a process, based on informative priors of its parameters, which allows one to incorporate into the estimation procedure the prior information on meaningful physical characteristics of the observed degradation process that is generally available to the analyst. Several different prior distributions are proposed, reflecting different degrees of knowledge on the observed phenomenon. A Monte Carlo Markov Chain technique is adopted for estimating the TW process parameters and some functions thereof. Finally, in order to show the feasibility of the proposed Bayesian estimation procedure and the flexibility of the TW process an example of application is developed.

Very recently, a new degradation process, namely the transformed gamma (TG) process, has been proposed in the literature to describe Markovian degradation processes whose increments over disjoint intervals are not independent, so that the degradation growth over a future time interval can depend both on the current age and the current state (degradation level) of the unit. This paper proposes a Bayesian estimation approach for such a process, that is based on prior information relative to the sign (positive or negative) of the correlation between the degradation increment and the current state or age of the unit. Several different prior distributions are then proposed, reflecting the knowledge of the analyst. A Markov Chain Monte Carlo technique, based on the adaptive Metropolis algorithm, is used for estimating the TG parameters and some functions thereof, such as the residual reliability of a unit, as well as for predicting future degradation growth. Finally, the proposed approach is applied to a real dataset consisting of wear measures of the liners of the 8-cylinder engine which equips a cargo ship.