Machine reliability modelling in manufacturing: A continuous-time state-dependent heterogeneous Markov chain approach

In practice, the maintenance schedule depends on the system states such as whether we have sufficient machines available for our workload or not. Therefore, in this Markov chain machine reliability model, we relaxed the fundamental assumption of classical reliability model that the up and down rates are fixed (machines are independent). The major contributions of this paper are as follows: (1) we developed a continuous-time heterogeneous Markov chain model with the linear and quadratic transition rate functions of system state to model a system with parallel machines; (2) we derived the mathematical framework and applied model reference adaptive search (MRAS) method to find the transaction rate function that best represents the system by minimizing the overall error in estimating the stationary probabilities of system states. Application case in solar panel industry shows that the resultant models are over 40% accuracy improvement comparing to that of the state-independent Markov chain model.