Replacement and standby redundancy policies in a deteriorating system with aging and random shocks

This study investigates the state-dependent maintenance policy in a multistate deteriorating production system with standby redundancy, assuming that the production system consists of one production unit and one single-server service center, and the key component of the production unit deteriorates over time. The key component deteriorates either from the current operating state to the next inferior operating state, due to aging, or from the current operating state to the failure state, due to a random shock. The deteriorating key component is replaced with a standby, according to a certain replacement policy, and sent to the service center for perfect repair; once completing the service, it joins the standbys for later production use. Both the sojourn time of a key component in each operating state, except the failure state, and the service time of a key component at the service center are assumed to be exponentially distributed. Taking into account the annual operating profit, measured in terms of production utilization and yield percentage of perfect items, and the annual operating costs, including the costs of key components and maintenance, this study jointly selects the operating state for replacing deteriorating key components and the level of standby redundancy in the system under the profit maximization objective. Numerical examples are given to illustrate the maintenance policies for systems with different transition probabilities in the deteriorating process, and the influence of transition probabilities on the maintenance policies is discussed.