This paper presents a decision-centered lifetime and reliability prognostics using a generic Bayesian framework. This generic Bayesian framework models and updates sensory degradation data, remaining life, and reliability using non-conjugate Bayesian updating mechanism. Thus, it continuously updates lifetime distributions of degraded system in realtime. Furthermore, the generic Bayesian framework eliminates dependency of evolutionary updating process on a selection of distribution types for the parameters of a sensory degradation model. The Markov Chain Monte Carlo (MCMC) technique is employed as a numerical method of non-conjugate Bayesian updating framework. While accounting for variability in loading conditions, material properties, and manufacturing tolerances over the population of system samples, different reliabilities will be identified for different samples. So, reliability distribution for an engineering system can be obtained and updated in a Bayesian format. The proposed Bayesian methodology is generally applicable for different degradation models and prior distribution types. The proposed methodology is successfully demonstrated with 26 resistors for the lifetime and reliability prognostics.