Robust Shewhart-Cusum Design for Monitoring Process Mean Using Repetitive Sampling

The present study initiates the use of repetitive sampling (RS) for CUSUM type statistics discussed by Riaz et al. (2017) and couples it with the Shewhart chart (termed as RS-SEC-TCC) by targeting two objectives, i.e. robustness to non-normality and detection of small to large mean shifts quickly. Individual and overall performance metrics have been used to show the RS-SEC-TCC’s supremacy over its competitors. The results indicate that the RS-SEC-TCC excels in identifying small to large mean shifts in both directions for symmetric and skewed distributions. When the process distribution is skewed, the RS-SEC-TCC demonstrates robustness by being free of the average run length (ARL) biased problem. The RS-SEC-TCC has also surmounted the weakness of the mixed EWMA-CUSUM TCC by enabling an earlier detection of a larger shift. In terms of overall performance metrics, the RS-SEC-TCC is adopted as a benchmark chart. By producing more out-of-control signals than its competitors in a real-world application, the RS-SEC-TCC proves its usefulness in practice. Consequently, the proposed RS-SEC-TCC will be a useful process monitoring tool that can be relied on by quality and industrial engineers