Effectiveness Indices for Statistical Process Control Chart Performance

The current standard practice in manufacturing industries and SPC textbooks only specify how to set up control limits and how to choose different run rules (such as the WECO rules) for control charts for process quality characteristic under monitoring. The cost modeling has also been developed in literature to determine the control chart settings for economic design; however, it has very limited applications in semiconductor manufacturing because the complexity of many process steps and multiple process equipments at each step made it nearly impossible to do cost modeling. For process characteristics with wide conformance specification, control limits width wider than 3 sigma has been widely in practical applications and a simple WECO rule of one point beyond control limits is popularly used. However, no index is designed to evaluate the effectiveness of control chart settings (the width of control limits). We define alarm types and the corresponding rates to distinguish alarms without root causes found during diagnostics from statistical false alarms. A new alarm type of non-OOC excursions is also defined and introduced. We use them to form indices and inequalities to evaluate whether the control limits are set too wide. When inexperienced engineers are unable to perform effective troubleshooting and root cause diagnostics, some true alarms are treated as false ones. These new indices and inequalities have made it possible to evaluate whether engineers need to improve their engineering troubleshooting skills. An overall index is also designed to judge the relative performance with different control limit settings.