Analytical formulae for computing the average time to signal (ATS) value for the exponentially weighted moving average (EWMA) cumulative count of conforming (CCC) chart using the Markov chain procedure are derived, as the performance of this chart is currently studied using simulation in the literature. Additionally, the variable sampling interval (VSI) EWMA CCC chart for monitoring the cumulative counts of items inspected until a nonconforming item is obtained in a high yield process and is developed to increase the sensitivity of the basic EWMA CCC chart. By using the Markov chain procedure, optimal parameters of the VSI EWMA CCC chart in minimizing the ATS value are obtained and provided to facilitate the chart's implementation in practice. It is found that the VSI EWMA CCC chart shows an impressive improvement over the basic CCC, VSI CCC, and EWMA CCC charts. An example using real data from an injection molding process producing micro‐prism array of an optical element is given to demonstrate the implementation of the VSI EWMA CCC chart in practice. The originality of this manuscript lies in the derivation of new Markov chain‐based analytical formulae for computing the ATS of the EWMA CCC chart and the incorporation of the VSI technique into the EWMA CCC chart to boost the out‐of‐control detection speed of the latter.

中文翻译：

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一种新的具有自适应控制方案的指数加权移动平均线图，适用于高产量工艺—在注塑工艺中的应用

推导了使用马尔可夫链程序计算指数加权移动平均值（EWMA）合格指数（CCC）图表的平均信号时间（ATS）值的分析公式，因为目前正在使用文献。此外，可变采样间隔（VSI）EWMA CCC图表用于监视检查的项目的累积计数，直到在高产量过程中获得不合格的项目为止，并开发该可变采样间隔以提高基本EWMA CCC图表的敏感性。通过使用马尔可夫链过程，可以获取并提供VSI EWMA CCC图的最佳参数以最小化ATS值，以方便在实践中实施该图。我们发现，VSI EWMA CCC图表相对于基本CCC，VSI CCC，和EWMA CCC图表。给出了一个使用注塑成型过程中产生光学元件微棱镜阵列的真实数据的示例，以演示VSI EWMA CCC图在实践中的实现。该手稿的独创性在于推导了用于计算EWMA CCC图表的ATS的新的基于马尔可夫链的分析公式，并将VSI技术纳入EWMA CCC图表以提高对SVMA CCC图表的失控检测速度。后者。