A new omnibus SPRT chart for monitoring process mean and variability based on the average number of observations to signal

The recent development of the omnibus sequential probability ratio test (OSPRT) chart marks a significant contribution to the advancement of joint monitoring schemes. As the OSPRT chart is a variable-sample-size control chart, practitioners often wish to understand its inspection efficiency, i.e. the number of observations it samples before producing a signal. In this article, we propose two enhanced optimization designs for the OSPRT chart based on the average number of observations of signal (ANOS) and expected value of the ANOS (EANOS) metrics under deterministic and unknown shift sizes, respectively. The ANOS metric is central to our design as it perfectly combines both the average run length (ARL) and the average sample number. A comparative analysis reveals that the OSPRT chart outperforms four benchmarking control charts in terms of the ANOS and EANOS metrics. Finally, an implementation of the OSPRT chart is presented with a ball shear test dataset.