A Study on the Laney p′ Control Chart with Parameters Estimated from Phase I Data: Performance Evaluation and Applications

The Laney p′ control chart is a new type of attribute control chart that can be applied in situations where the process exhibits either overdispersion or underdispersion. While it has gained acceptance in the industry, there is still limited knowledge about its effectiveness in detecting process variation. It is well known that before applying a control chart, understanding its performance is crucial, especially when the parameters of the control chart need to be estimated from historical data. In this study, we used simulations to investigate the ability of the Laney p′ control chart to detect process variations when the parameters are estimated. We designed appropriate experiments to assess the impact of overdispersion on the average run length (ARL) performance. In this study, we assumed that the overdispersion comes from the variation in the mean fraction nonconforming of each sample. The mean value varies according to a uniform distribution. This study evaluated the performance of the Laney p ′ control chart using the average of the ARL (AARL) and the standard deviation of the ARL (SDARL). Additionally, real-world data were utilized to illustrate the practical applications of the Laney p ′ control chart in the PCB and IC substrate industries. The research findings can serve as valuable guidance for practical implementation.