Modeling and optimal control of deteriorating production processes

Most systems in the real world are subject to deterioration. Modeling and optimal control of deteriorating production processes such as tool Wear and tool failure have been important research areas. When (1) the operating conditions of the deteriorating systems Vary (deterministicdly or stochastically), or (2) the deteriorating processes are non-homogeneous (characterized by increasing mean and increasing variance), or (3) if we want to incorporate the information representing the operating conditions of the deteriorating systems from condition monitoring such as vibration signals into the modei, the problem becomes

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