A general model for the economic-statistical design of adaptive control charts for processes subject to multiple assignable causes

Fully adaptive control charts are efficient statistical process control means to monitor a quality characteristic affecting the outcome of a manufacturing process. Usually, the performance of these adaptive charts is investigated in processes characterised by the possibility of the occurrence of a single assignable cause. However, this assumption is frequently far from reality, because a process shift to the out-of-control condition can be the consequence of several assignable causes, which can occur at the same time or independently. In this paper, we investigate the economic-statistical design of a variable-parameter (Vp) Shewhart control chart monitoring the process mean in the presence of multiple assignable causes. We develop a Markov chain that models the occurrence of several assignable causes leading to progressive process deterioration and calling for different corrective actions. A benchmark of examples has been generated to compare the performance of the Vp control chart with other adaptive control charts and the fixed-parameter control chart. The obtained results reveal the economic superiority of the Vp control chart.