Hidden markov models in reliability and maintenance

Abstract

Although the hidden Markov models (HMM) are very popular in many applied areas their use in reliabil- ity engineering is limited. Problems such as the selection of the HMM model by choosing the appropriate number of states, or problems of prediction of failures have not been widely covered in the literature. This paper is concerned with the use of HMMs where the state of the system is not directly observable and instead certain indicators of the true situation are provided via a control system. A hidden model can provide key information about the system dependability such as the failed component of the sys- tem, the reliability of the system and related measures. A maximum-likelihood estimator of the system reliability is obtained and its asymptotic properties are studied. Finally, the maintenance of the system is considered in this context and new preventive maintenance strategies are defined and their efficiency is measured in terms of expected cost. To prove the finite sample performance of the methodology, an extensive simulation study is developed.