Abstract: As an important tool to improve product quality, control chart plays a vital role in quality monitoring. Traditional control charts typically assume that the process follows known distributions such as normal distribution, binomial distribution, Poisson distribution, etc., and such control charts require a sufficient number of samples to estimate parameters, also known as parameter control charts. But, with the rapid development of the current technological environment and the increasing demand for personalized products, small batch production has gradually become an important production mode to meet diverse market demands. In a small batch production mode, the sample size often cannot meet the requirements of the parameter control chart, resulting in the traditional control chart no longer to be applicable.
In order to adapt to the characteristics of small batch production, non-parametric control charts are proposed and widely used. This control charts have the advantage of not relying on accurate estimation of process distribution parameters, and can still play a role in limited sample sizes. However, non-parametric control charts are generally weak at monitoring abnormal process shifts. In order to improve the monitoring efficiency of non-parametric control chart, this paper combines dynamic control charts and memory-based control charts, and constructs a dynamic non-parametric Exponentially Weighted Moving Average Sign (EWMA-SN) control chart using Variable Sampling Interval (VSI).
In the design of control charts, being statistical and being economic play equally important and irreplaceable roles as the main indicators for evaluating the performance of control charts. Therefore, this paper uses the Markov chain method to calculate the Average Product Length (APL) and the average product quality cost of the control chart. As a statistical evaluation index, APL in out-of-control state represents the performance of the control chart in actual operation, while the average quality cost reflects the cost-effectiveness of the control chart from an economic point of view. Using both as common objective functions, a multi-objective optimization design model for non-parametric VSI EWMA-SN control charts is constructed and the effectiveness of the model in practical applications is verified through specific examples and sensitivity analysis. Finally, by comparing and analyzing several other existing non parametric control chart methods, the results show that the VSI EWMA-SN control chart has significant advantages in both statistical and economic aspects.
In this study, only the variable sampling interval design is carried out on the model, and the sample size remains fixed. The subsequent study will consider the variable sample size design of the model to achieve a more comprehensive dynamic optimization.

Key words: small batch production, non-parametric EWMA control chart, variable sampling interval, multi-objective optimization

摘要： 非参数控制图是一类适用于小批量生产模式的过程质量控制方法,具有不依赖过程分布参数的准确估计的优点,但对异常波动的监控能力通常较弱。为了提高非参数控制图的监控效率,本文结合动态控制图和记忆型控制图,采用可变抽样间隔(Variable Sampling Interval, VSI)构造了一种动态非参数指数加权移动平均符号(Exponentially Weighted Moving Average Sign,EWMA-SN)控制图,基于马尔科夫链方法计算了该图的统计性能评价指标平均产品长度(Average Product Length,APL)和经济性能评价指标平均产品质量费用,在此基础上设计了非参数VSI EWMA-SN图的多目标优化模型,运用具体的算例和主要控制图参数的灵敏度分析说明了该模型的应用。最后,与其它几种已有的非参数控制图方法进行了比较分析。结果表明本文的VSI EWMA-SN图多目标优化设计在统计和经济性能两方面都具备更为良好的效果。

关键词: 小批量生产, 非参数EWMA控制图, 可变抽样区间, 多目标优化