Real-time Condition-monitoring: The Impact of Bayesian Update on Failure-time Distribution

Many classic age replacement policies rely on the assumption that the time-to-failure distribution has an increasing failure rate. In addition, many commonly used probability distributions possess the increasing failure rate property, including the Normal distribution and the Weibull distribution with shape parameter greater than one. However, significant recent research has considered how real-time sensor data, obtained through condition monitoring, can be used to periodically update the time-to-failure distribution of a functioning device. For example, in some proposed approaches, the time-to-failure distribution is computed using Bayesian updating given the observed sensor data. In this research, we investigate how the use of Bayesian updating changes the characteristics of the failure rate associated with the time-to-failure distribution. For example, while it is well-known that the Exponential time-to-failure distribution has a constant failure rate, we demonstrate that its Bayesian-updated time-to-failure distribution has a decreasing failure rate (DFR).