The SPRT chart for monitoring a proportion

A control chart based on applying a sequential probability ratio test (SPRT) at each sampling point is considered for the problem of monitoring a process proportion p. This SPRT chart can be applied in situations in which items are inspected one by one, and the results of each inspection can be conveniently recorded before the next item is inspected. Some corrected diffusion theory approximations are given for the statistical properties of the SPRT and the SPRT chart. These approximations are very accurate and provide a simple method for designing an SPRT chart for practical applications. The sample size for the SPRT chart at a particular sampling time depends on the observations at that time, but the chart can be designed to have a specified average sampling rate when the process is in control. When there is a small shift in p, the average sampling rate per unit time will increase, but for a large shift in p the average sampling rate will decrease. For a given in-control average sampling rate and a given false alarm rate, the SPRT chart will detect changes in p much faster than the standard, p-chart, which has traditionally been used for monitoring p. The SPRT chart will also detect changes in p much faster than the CUSUM chart for p. Thus, the SPRT chart can be used in place of traditional control charts to provide faster detection of changes in p or to reduce the sampling effort required to provide a given detection capability.