A primary concern in product design is ensuring high system reliability amidst various uncertainties throughout a product life-cycle. To achieve high reliability, uncertainty data for complex product systems must be adequately collected, analyzed, and managed throughout the product life-cycle. However, despite years of research, system reliability assessment is still difficult, mainly due to the challenges of evolving, insufficient, and subjective data sets. Therefore, the objective of this research is to establish a new paradigm of reliability prediction that enables the use of evolving, insufficient, and subjective data sets (from expert knowledge, customer survey, system inspection & testing, and field data) over the entire product life-cycle. This research will integrate probability encoding methods to a Bayesian updating mechanism. It is referred to as Bayesian Information Toolkit (BIT). Likewise, Bayesian Reliability Toolkit (BRT) will be created by incorporating reliability analysis to the Bayesian updating mechanism. In this research, both BIT and BRT will be integrated to predict reliability even with evolving, insufficient, and subjective data sets. It is shown that the proposed Bayesian reliability analysis can predict the reliability of door closing performance in a vehicle body-door subsystem where the relevant data sets availability are limited, subjective, and evolving.