A novel condition-based maintenance framework for parallel manufacturing systems based on bivariate birth/birth–death processes

This paper addresses a condition-based maintenance scheduling for a continuously monitored manufacturing system. In such a system, each unit is subject to deterioration, which is modeled as a continuous-time Markov process with two working states and a failure state. Maintenance is initiated when the system state falls into a state with a pre-specified number of failed units. We develop a novel framework to find the optimal policy using a tractable bivariate Birth/Birth–Death process and renewal theory. The optimal maintenance policy is derived by minimizing the long-run expected average cost per unit time. We further obtain the mean time to perform maintenance by obtaining the mean first passage time to states where maintenance is initiated. The parameters of the birth/birth–death process are assumed to be unknown, and maximum likelihood method is employed to obtain parameter estimates based on the number of units observed in each state at different times. Numerical examples are provided to illustrate the proposed optimization model. We also conduct a simulation study to see the effect of the proposed preventive maintenance policy on the expected profit over a one year interval.