基于预防维修的可变抽样区间泊松EWMA控制图经济设计

doi:10.12005/orms.2023.0292

摘要/Abstract

摘要： 现代质量控制的核心技术和方法始终围绕着如何提高监控效率和降低控制成本问题而展开。统计过程控制是一种常用的质量控制方法,其重要的工具——控制图对过程中的质量特性值进行统计并描点达到监控过程质量状态的目的。控制图的设计方法将会对产品过程的监控效率和控制成本产生较大影响。针对只考虑传统控制图参数固定以及控制图统计设计的情形,传统的缺陷数c控制图基于泊松分布建立以监控制造过程中产品的缺陷数。为了降低控制过程成本并提高缺陷数c控制图的监控效率,研究预防维修策略下可变抽样区间(VSI) EWMA图的经济设计问题。首先,建立泊松分布下VSI EWMA控制图的经济模型。其次,令单位时间的损失成本函数最小得到经济模型的最优解。以化工建材行业为例,说明如何根据预防维修策略下所构建的控制图经济模型得到最优参数。然后,为得到设计参数与模型参数的影响关系,对经济模型灵敏度分析。最后,对经济模型进行最优性分析验证其优越性。

关键词: EWMA控制图, 可变抽样区间, 经济设计, 预防维修策略

Abstract: The core techniques and methods of modern quality control have always been centered on how to improve monitoring efficiency and reduce the control cost. Statistical process control is a commonly used quality control method, and the control chart is an important tool for monitoring and ensuring the quality of the process. The design method of control charts has a large impact on the efficiency of monitoring and controlling the production process and control cost. The statistical design of the control charts is mainly based on statistical standards of the control chart, and although it takes into account the statistical properties of the control chart, it does not consider the economic benefits of the control charts.
From an economic perspective, the cost of investigating alarm signal, producing defective products, sampling and testing and correcting abnormity cause influence the parameters design of control charts. Therefore, it is logical to design the control chart from an economic point of view. For the case where only the parameters of the traditional control chart are considered to be fixed and the statistical design of the control chart is considered, the traditional control chart for the number of defects c is proposed based on the Poisson distribution to monitor the number of defects in the product during the manufacturing process. In order to improve the efficiency of defect count c control charts for process monitoring and to reduce the cost of the control process, economic design of variable sampling intervals (VSI) EWMA (exponentially weighted moving average) control chart and preventive maintenance strategy under Poisson distribution is discussed in this paper.
Firstly, an economic model of VSI EWMA chart based on preventive maintenance strategy and quality loss function under Poisson distribution is developed.Secondly, the loss cost function per unit time is minimized and the optimal solution of the economic model is obtained by using genetic algorithm. Taking the chemical building materials industry as an example, it shows how to determine the optimal solutions of the parameters based on the VSI Poisson EWMA control chart economic model established under the preventive maintenance strategy.Thirdly,a sensitivity analysis of the developed economic model is performed to obtain the relationship between the influence of the control chart design parameters according to the variation of the model parameters, and the results of and the analysis are as follows: (1)The sample size decreases with the increasing shift in process mean. (2)The lower control limit coefficient decreases with the increase of the frequency of abnormal causes and the average cost of finding and correcting an abnormal cause. (3)The long sampling interval decreases with the increase of process mean shift. (4)The lower warning limit coefficient decreases with increasing frequency of abnormal causes. (5)The smoothing coefficient increases with the decreasing shift in process mean shift. (6)The loss cost function per unit time increases with the increase of the sampling cost per sample, the average time of the correction process and the loss when the product is unqualified, and decreases with the increase of the process mean fluctuation. Finally, the superiority of the developed economic model is verified by making optimality analysis, and the VSI EWMA chart designed based on the economic model developed in this paper was superior to the VSI EWMA control chart designed by the statistical method, and has a smaller expected loss cost per unit time.

Key words: exponentially weighted moving average (EWMA) control chart, variable sampling intervals policy, economic design, preventive maintenance strategy

中图分类号:

O213.1

薛丽, 曹逗逗, 王秋语. 基于预防维修的可变抽样区间泊松EWMA控制图经济设计[J]. 运筹与管理, 2023, 32(9): 107-113.

XUE Li, CAO Doudou, WANG Qiuyu. Economic Design of EWMA Control Charts with Variable Sampling Intervals for Monitoring Poisson Distributions Based on Preventive Maintenance[J]. Operations Research and Management Science, 2023, 32(9): 107-113.

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