New Insights on the SPRT Control Chart when the Process Parameters are Unknown

In the design of the sequential probability ratio test (SPRT) chart, it is customary to adopt a set of prescribed process parameters (i.e., process mean and standard deviation). In recent years, there has been increasing consensus on the importance of investigating performances of the control charts assuming that the process parameters are unknown. This leads to the norm of estimating in-control process parameters from the historical Phase-I data set, and applying them in place of the true mean and standard deviation of the process data. Nonetheless, the use of estimated in-control process parameters is shown to have negative consequences on control chart's performances, especially when the Phase-I data is limited. In this paper, we provide a fresh look at the SPRT chart with estimated process parameters, both when the processes are out-of-control and in-control. We analyze the performances of the SPRT chart with known and estimated process parameters, as well as provide concise insights from three different perspectives. Results show that, when the Phase-I sample size and process mean shift are small, the average and standard deviation of the time to signal tend to vary considerably from those with known process parameters. Besides, we notice that the in-control performances of the SPRT chart with estimated process parameters worsen when a large inspection rate is used. Therefore, we recommend using a large number of Phase-I samples in parameter estimation and/or a small inspection rate to attain desirable chart's performances.