Synthetic control chart with curtailment for monitoring shifts in fraction non-conforming

Abstract

The integration of the curtailment method with control charts considerably improves the detection speed by signaling an out-of-control condition prior to the inspection of the whole sample. To date, few research works have focused on the incorporation of the curtailment method to improve the performance of control charts. Thus, this paper incorporates the curtailment approach with the synthetic chart to propose a synthetic control chart with curtailment (Curt_Syn) for detecting upward shifts in the fraction nonconforming, p. We compared the newly developed Curt_Syn chart with the synthetic, exponentially weighted moving average (EWMA), cumulative sum (CUSUM), EWMA with curtailment (Curt_EWMA), and CUSUM with curtailment (Curt_CUSUM) charts. From an overall perspective, the results reveal that the Curt_Syn chart surpasses the synthetic chart by 38% under various conditions. For all p shifts, the Curt_Syn chart outperforms the CUSUM and EWMA charts. When the p shift is large, the Curt_Syn chart is superior to the Curt_CUSUM and Curt_EWMA charts. To demonstrate the implementation of the Curt_Syn chart, an illustrative example is provided.

Economic statistical model of the np chart for monitoring defectives

“…The out-of-control ARL can be defined as the average number of samples required to detect a process shift after it occurs 10 – 12 . Similarly, the out-of-control ATS can be defined as the average time required to detect a process shift after it occurs 13 – 15 . The establishment of a cost-related design of control charts is needed due to the lack of any measure that directly represents costs.…”