Optimizing P-Chart Performance Using a Percentage-Based Framework: Application to Nonconforming Items in the Manufacturing Sector

The control chart approach in industrial processes often faces significant challenges in accurately assessing the in-control (IC) and out-of-control (OC) performance of a process because of the limitations of conventional performance metrics. Traditional methods, such as the average run length (ARL)-based p-chart, may not effectively capture the complexities of run-length (RL) distributions, particularly in sectors with demanding performance standards. This study addresses these challenges by introducing a percentile-based (PB) p-chart approach, which guarantees specific IC and OC performance with predefined probabilities. The proposed approach overcomes the limitations of conventional methods, treating the ARL-based p-chart as a special case within the broader PB framework. By imposing constraints on the RL distribution, it is possible to guarantee predetermined probabilities for both IC and OC performance. This ensures that the IC run length ( $\text {RL}_{\text {IC}}$ ) exceeds the desired value, whereas the out-of-control run length ( $\text {RL}_{\text {OC}}$ ) remains below the desired threshold. The effectiveness of this p-chart scheme is shown through simulations and various numerical examples. The numerical results show that the p-chart based on the proposed scheme outperforms the existing methods and minimizes false alarms. To ease the computation of the optimization used in this design, software support of the proposed approach is provided for public use through a freely accessible R library pbcc. Finally, the implementation procedure of the proposed design is also demonstrated using two real-data examples. The numerical results show that the p-chart based on the proposed scheme outperforms existing methods, with a 150% improvement in the water bottle manufacturing process and a 45% improvement in the cardboard filling and packing process, while also minimizing false alarms.