Dynamic reliability and sensitivity analysis based on HMM models with Markovian signal process

The main objective of this paper is to build stochastic models to describe the evolution-in-time of a system and to estimate its characteristics when direct observations of the system state are not available. One important application area arises with the deployment of sensor networks that have become ubiquitous nowadays with the purpose of observing and controlling industrial equipment. The model is based on hidden Markov processes where the observation at a given time depends not only on the current hidden state but also on the previous observations. Some reliability measures are defined in this context and a sensitivity analysis is presented in order to control for false positive (negative) signals that would lead to believe erroneously that the system is in failure (working) when actually it is not. System maintenance aspects based on the model are considered, and the concept of signal-runs is introduced. A simulation study is carried out to evaluate the finite sample performance of the method and a real application related to a water-pump system monitored by a set of sensors is also discussed.