Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)

First Advisor

Tang Kwei

Second Advisor

Linguo Gong


The traditional control chart method of SPC is a popular tool for monitoring a production process. The method involves randomly drawing a sample of finished items from the process at every equal-time interval to check the product quality and assess the process condition. Because of recent technological advances in computer automation, many kinds of on-line inspection and monitoring equipment, such as sensors, have been developed. This research proposes a two-phase method to monitor the production process during manufacturing operations. Basically, this method is a combination of an on-line sensor and a control-chart method. In the first phase, if the total number of sensor measurement values exceeding a preset setpoint is larger than a cutoff level, a sensor warning signal is given and a sample is drawn immediately from the process to assess the process condition. In the second phase, if the sampling mean falls outside the action limit of the mean control chart, then we conclude that the process may have shifted to the out-of-control state. In this situation, the process is stopped for necessary adjustments. We assume that the occurrence of sensor warning signals follows a Poisson distribution. An expected cost model has therefore been established in terms of three decision variables; namely, sensor setpoint, sampling size, and action limit. Many analytical results are derived. We find that the proposed two-phase method will generate more average true warning signals per unit time and will result in a lower expected cost per cycle than the method derived from a single-sensor phase model and a single control method.