An Integrated Optimal-Gicp Design for the SPRT Control Chart with Estimated Process Parameters Based on the Average Number of Observations to Signal

As a variable-sample-size control scheme, the sequential probability ratio test (SPRT) chart is favoured due to its sensitivity and high sampling efficiency. It is frequently documented that the SPRT chart inspects only a small number of observations at each sampling stage, making the said chart extremely appealing to quality engineers. In the current literature, most developments of the SPRT chart are established based on the average run length and average time to signal metrics. However, these metrics do not consider sampling efficiency. In this paper, we develop two optimal designs of the SPRT chart, based on (i) the average value of the average number of observations to signal (AANOS) and (ii) the expected value of the AANOS, with consideration of Phase-I process parameter estimation. We develop a model that integrates the concept of optimization and the guaranteed in-control performance (GICP) framework to neutralize the adverse effects of parameter estimation. Results show that the proposed optimal-GICP design preserves satisfactory out-of-control performances for moderate and large mean shifts, while keeping the false alarm rates at reasonably low levels. Finally, we illustrate an example of the SPRT chart with estimated process parameters for monitoring loop height measurements from a wire bonding dataset.