Zachary G. Stoumbos
Rutgers, The State University of New Jersey Graduate School of Management
Department of Management Science and Computer Information Systems
In recent years, variable sampling interval (VSI) control charts have been intensively investigated. In contrast to traditional fixed sampling interval (FSI) control charts, VSI charts vary the sampling interval as a function of the data. VSI charts detect many process changes substantially faster than their FSI counterparts. A disadvantage, however, of VSI charts as recently formulated is that the advance prediction of sampling times is impossible for more than the next sample. A control chart is proposed which applies a generalized sequential probability ratio test (SPRT) at fixed sampling intervals, the GSPRT chart, to monitor the mean of a process with a normal distribution. A natural modification of the GSPRT chart is also proposed in which samples are always taken at pre-specified, equally spaced fixed times, with additional samples taken between these times as indicated by the data. These times would typically be determined by administrative considerations and efficiency requirements of the process. The integral equation approach is adapted for the evaluation of properties of both the unmodified and modified versions of the GSPRT chart, such as average run length (ARL), average time to signal (ATS), and steady-state ATS (SSATS). Comparisons are made between the performance of the two versions of the GSPRT chart and the FSI and VSI X-bar and cumulative sum (CUSUM) charts. Both versions of the GSPRT chart are found to be highly efficient and have administrative advantages.
This research was conducted jointly with Professor Marion R. Reynolds, Jr. from the Virginia Tech Department of Statistics.
Seminar to be held in Room 107, 24 Hillhouse Ave at 4:15 pm