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
( RLIC ) exceeds the desired value, whereas the out-of-control run length ( RLOC )
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.
