Beyond Regular SPC: Bridging the \(C_{pk}\) Capability Index for (a)Symmetric Data

The advancement of technology has increased competitiveness, especially in the manufacturing industry. Alongside Statistical Process Control (SPC), capacity indices are tools used to measure the quality of processes and are useful for establishing standards in manufacturing products. This study was motivated to propose a new control chart based on the capability index \(C_{pk}\), which is particularly useful for real-time monitoring with respect to short time frames and longitudinal studies. Our methodology proposes a graphical monitoring tools that is obtained by utilizing the rolling capability index with standard distributions (Normal, Gamma, or Weibull) and bootstrap intervals based on closed-form estimators. Simulations and real-world applications demonstrated the utility of our framework, which is computationally inexpensive and applicable to real-time monitoring (useful for longitudinal or time-varying processes), showing that modified-Cpk for asymmetric processes is more accurate than point estimation based on normality. Moreover, the exemplification data from a Chocolate Factory showed an acceptable process trend in 25% of the observed rolling-windows (from the first modified-Cpk estimations), versus the normal-based that barely detected this pattern (only one in-sample period). That means, a reduction of \(\approx 22\%\) on the quality improvement interventions (translated as false alarms).