### Statistical Process Control

Session Chair: Nien-Fan Zhang, NIST**Control Charts for Poisson Count Data with Varying Sample Sizes**

Anne G. Ryan and William H. Woodall

Virginia Tech

Abstract: Various cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts have been recommended to monitor a process with Poisson count data when the sample size varies. We evaluate the ability of these CUSUM and EWMA methods in detecting increases in the Poisson rate by calculating the average run length (ARL) performance for the charts. Our simulation study indicates that the CUSUM chart based on the generalized likelihood ratio method is best at monitoring Poisson count data when the sample size varies randomly and it is of interest to detect small increases in the rate quickly. We also propose a new EWMA method which has good ARL performance.

**A Review of Control Charts for High Quality Processes**

John L. Szarka, III and William H. Woodall

Virginia Tech

Abstract: High quality processes have been evaluated using various techniques in statistical process control (SPC). The high quality process data often consist of information on items classified as conforming (non-defective) or nonconforming (defective) from a Bernoulli process, where the probability of a nonconforming item is so small, that it can be conveniently measured in parts per million (ppm) or parts per billion (ppb). This area of SPC is also applied to health-related monitoring, where the incidence rate of a rare disease is of interest. In these applications, standard Shewhart control charts based on the binomial distribution are no longer able to effectively detect changes in the nonconforming rate. In this presentation, we review some of the methods implemented for these scenarios and present ideas for future work in this area.

**A Resetting Design of the Manufacturing Process for the EPC and the SPC**

Changsoon Park

Chung-Ang University

Abstract: In every manufacturing process, the process control activity, such as EPC and SPC, has been implemented to maintain the quality of the products at the designated level. During the implementation of the process control activity, the process will be reset periodically by reinitializing its manufacturing conditions before the process will be too much deteriorated.

In the EPC design, the continual use of the controller to adjust the process level to target tends to increase the variability of the products although it has been successful in maintaining the mean close to target. The reset of the process will return the controller to the initial setting and will reduce the variance of the quality characteristic with some reset cost.

In the SPC design, engineers try to search special causes when a signal is given. In a multistage manufacturing process (MMP), the measurement of the quality is available only after a group of the unit processes has passed. In such cases the search of special causes is often unsuccessful and engineers may have wrong judgments for the given signals. There can be three cases of wrong judgments. Case 1: The signal is true but engineers fail to find the special cause. Case 2: The signal is false but engineers regard that they find the special cause due to wrong identification. Case 3: The signal is false but engineers regard that they failed to find the special cause. Since searching special causes is too complicated in MMPs to make a correct judgment every time and engineers prefer always correct decisions rather than some incorrect ones, resetting the process is proposed when a signal is given regardless of true or false signal. The resetting of the process will avoid such wrong judgments and make engineers confident to the control scheme.

In this research the resetting design is studied for the EPC and the SPC schemes with respect to the economic sense. The process will be reset when the reset statistic exceeds the bound. The appropriate reset statistic is the controller for the EPC and the control chart statistic for the SPC. The bound will be determined according to the economic efficiency of the reset procedure.

**A Follow-Up Change Point Estimation Procedure to Identify the Time of a Step Change in Time Between Events (TBE) Control Charts**

Eralp Dogu

Dokuz Eylul University

Abstract: Statistical process control efforts are considered to ensure high-quality production and reduce costs in the competitive environment of business. The signal issued by a control chart triggers the process to identify and eliminate the cause(s) of the out of control situation. Knowing the time of the change simplifies the search for and identification the special cause. Identifying the time of the step change is vital for high-yield processes for both improvement and deterioration cases. In this study, a considerably effective change point model based on maximum likelihood estimation is introduced to control and monitor time between events data which follows exponential and gamma distribution. After the Cumulative Quantity Control (CQC) or CQC-r charts issue a signal, the procedure starts and identifies the most likely time of the step change. It is quite beneficial for process professionals to monitor the process and detect the time of the process step change.