Abstract: As an effective statistical quality management tool, control charts have been widely used in production and service processes. In recent years, there have been many studies on optimization and reconstruction of control charts to improve monitoring performance or reduce application costs. Control charts can generally be divided into two types: metric and count. The metric type is for continuous variables and requires more accurate measurements, while the count type is for discrete variables and only requires statistics on the number of pieces or points, so the measurement cost is often lower. Therefore, when the measurement cost of a quality characteristic is high or the time required is long, applying count control chart to monitor continuous variables can be an effective method to reduce costs. np_x chart is a method of monitoring continuous quality characteristics using a non-conforming product quantity control chart. Compared to traditional Shewhart control charts, it has lower quality monitoring costs but poorer detection effects on abnormal shifts.
In order to transform the measurement of continuous variables into simple and fast count type measurements, a simple measurement device with upper and lower warning limits is constructed. Based on the number of samples passing through the measurement device in a set of samples, a count type statistic following a binomial distribution is constructed. In order to improve control chart monitoring efficiency of process abnormal shifts, a variable sampling interval exponential weighted moving average np_x (VSI-EWMA-NPX)control chart is constructed by combining the design ideas of dynamic control chart and exponential weighted moving average control chart, which can achieve high detection ability for abnormal shifts at a lower quality cost. On this basis, the statistical performance and economic performance of the control chart are evaluated using relatively accurate average product length(APL) and unit product average quality cost. The calculation methods of these two indicators are studied, and an economic-statistical multi-objective optimization design model of this chart is constructed using both as objective functions. A specific example is used to illustrate the calculation steps of the optimized design model, and compared and analyzed with several existing control chart methods. The results show that, regardless of the abnormal changes in process mean or standard deviation, the optimized design scheme proposed in this paper has significant advantages in monitoring efficiency and quality cost compared to other control chart methods.
Due to the fact that the design model in this article has multiple non inferior solutions, quality management personnel can choose any one of them as the design solution based on practical application needs or their own preferences. In addition, due to the requirement of np_x chart for the sample size that remains unchanged, the sampling strategy in this article only dynamically adjusts the sampling interval, so future research will consider breaking this limitation and constructing an EWMA-NPX chart design method where multiple control chart parameters can be adaptively adjusted based on the sampling results.

Key words: np_x chart, EWMA chart, dynamic chart, average product length, multi-objective optimization

摘要： 为了提高np_x图对过程异常波动的监控效率,结合可变抽样间隔(VSI)动态控制图和指数加权移动平均(EWMA)图的设计方法,构造了一种能够以较低的质量成本实现对异常波动的具有较高检测能力的VSI-EWMA-NPX控制图,研究了平均产品长度(APL)和单位产品平均质量成本的计算方法,并由此构建了VSI-EWMA-NPX图的经济统计多目标优化设计模型。通过一个具体的算例说明了该优化设计模型的计算步骤并与已有的几种控制图方法进行比较,结果表明:本文提出的优化设计方法在统计性监控效率和经济性质量成本两方面都具有良好的表现。

关键词: np_x控制图, EWMA图, 动态控制图, 平均产品长度, 多目标优化