Steady-state-optimal adaptive control charts based on variable sampling intervals

Variable sampling interval (VSI) control charts vary the sampling rate adaptively as a function of the data coming from the process in order to reduce the detection delay of process changes. Zero-time performance refers to the detection delay of a process change that is present during the onset of the chart at time zero. Steady-state performance refers to the detection delay of a process change that occurs after the chart has been operating for some time. The zero-time performance of a VSI control chart can differ considerably from the chart's steady-state performance, which is generally more important than the zero-time performance. We develop an efficient quadratic-programming algorithm for the construction and investigation of steady-state-optimal sampling policies for various VSI charts. We show that a steady-state-optimal VSI scheme is fundamentally different from the respective zero-time-optimal VSI scheme, and recommend VSI policies based on two sampling intervals for the various types of control charts considered.

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