Optimal integrated process control and maintenance under general deterioration

We develop an integrated Statistical Process Control (SPC) and preventive maintenance (PM) model for three-state processes (two operational states and a non-operational failure state) taking into account the interrelation between quality degradation and proneness to complete failure. No restriction is placed on the distributions of the times to quality shifts and failures and different types of inspection policies and tools are allowed signifying a wide practical applicability of the model. The proposed scheme leads to significant economic improvement compared to: (a) independently obtained SPC and PM policies, which treat quality shifts and failures in isolation, and (b) approximate models, which assume Markovian deterioration.