可变抽样区间和样本容量的非正态EWMA控制图经济设计

doi:10.12005/orms.2022.0051

运筹与管理 ›› 2022, Vol. 31 ›› Issue (2): 111-118.DOI: 10.12005/orms.2022.0051

可变抽样区间和样本容量的非正态EWMA控制图经济设计

薛丽^1,2, 李聪凯¹, 贾元忠¹

1.郑州航空工业管理学院管理工程学院,河南郑州 450046;
2.天津大学管理与经济学部,天津 300072

收稿日期:2020-06-15 出版日期:2022-02-25 发布日期:2022-03-11
作者简介:薛丽(1981-),女,河南项城人,硕士生导师,博士,副教授,研究方向:质量工程;李聪凯(1994-),男,汉族,河南焦作人,硕士研究生,研究方向:质量工程;贾元忠(1995-),男,河南商丘人,硕士研究生,研究方向:质量工程。
基金资助:
国家自然科学基金资助项目(71701188,71902138,71871204);教育部人文社科项目(21YJC630151);中国博士后科学基金资助项目(2016M601266);河南省科技攻关计划(202102310638);郑州航空工业管理学院研究生教育创新计划基金(2021CX09,2021CX10)

Economic Design of Variable Sampling Interval and Sample Size EWMA Control Chart under Non-normal Distributions

XUE Li^1,2, LI Cong-kai¹, JIA Yuan-zhong¹

1. School of Management Engineering, Zhengzhou University of Aeronautics, Zhengzhou, 450046, China;
2. College of Management and Economics, Tianjin University, Tianjin, 300072, China

Received:2020-06-15 Online:2022-02-25 Published:2022-03-11

摘要/Abstract

摘要： 为了降低过程控制成本和提高监控效率,针对质量特性值不服从正态分布的情况,研究可变抽样区间和样本容量(VSSI)的指数加权移动平均(EWMA)控制图的经济设计问题。首先对监控非正态分布的EWMA控制图进行抽样区间和样本容量变化设计;其次建立VSSI 非正态EWMA控制图的经济模型,通过使费用成本函数最小得到控制图的最优设计参数组合;然后给出工业中的一个例子,用遗传算法对经济模型搜寻最优解;接下来对经济模型进行灵敏度分析,得出控制图费用参数与设计参数之间的影响关系;最后通过最优性分析,得出所建立的VSSI 非正态EWMA控制图的经济性优于VSI、VSS非正态EWMA控制图。

关键词: 可变抽样区间和样本容量, 指数加权平均(EWMA)控制图, 经济设计, 非正态分布

Abstract: To reduce the costs of process control and improve the monitoring efficiency of control chart, the economic design of exponential weighted moving average (EWMA) control chart with variable sampling intervals and sample size (VSSI) for monitoring non-normal data is proposed. Firstly, using Burr distribution to approximate various non-normal distributions, EWMA control chart with variable sampling intervals and sample size is proposed. Secondly, economic model of VSSI EWMA control chart under non-normal distributions was developed, the optimal design parameter combination of the control chart is obtained, such that the total expected cost is minimized. Thirdly, the genetic algorithms (GA) will be used to search for the optimal values of parameters of the VSSI EWMA chart for non-normal data, and an example is provided to illustrate influence relationship between the cost parameters of the control chart and the design parameters. Finally, through the optimality analysis, it is concluded that the economy of the established VSS Inon-normal EWMA control chart is better than that of VSI and VSS non-normal EWMA control chart.

Key words: variable sampling interval and sample size, EWMA chart, economic design, non-normal data

中图分类号:

O213.1

薛丽, 李聪凯, 贾元忠. 可变抽样区间和样本容量的非正态EWMA控制图经济设计[J]. 运筹与管理, 2022, 31(2): 111-118.

XUE Li, LI Cong-kai, JIA Yuan-zhong. Economic Design of Variable Sampling Interval and Sample Size EWMA Control Chart under Non-normal Distributions[J]. Operations Research and Management Science, 2022, 31(2): 111-118.

参考文献

[1] Saccucci M S, Amin R W, Lucas J M. Exponentially weighted moving average control schemes with variable sampling intervals[J]. Communications in Statistics-Simulation and Computation, 1992, 21(3): 627-657.
[2] 吉明明,赵选民,唐伟广可变抽样区间的非正态EWMA均值控制图[J].系统工程,2006,24(11):114-119.
[3] 薛丽.可变抽样区间二项EWMA控制图[J].数理统计与管理,2016,35(6):1038-1044.
[4] Tang A, Castagliola P, Sun J S, Hu X L. An adaptive exponentially weighted moving average chart for themean with variable sampling intervals[J]. Quality and Reliability Engineering International, 2017, 33: 2023-2034.
[5] Tran K D, Nguyen H D, Nguyen T H, Tran K P. Design of a variable sampling interval exponentiallyweighted moving average median control chart in presenceof measurement errors[J]. Quality and Reliability Engineering International, 2021, 37: 374-390.
[6] Reynolds M R, Arnold J C. EWMA control charts with variable sample sizes and variable sampling intervals[J]. IIE Transactions, 2001, 33: 511-530.
[7] Chang Y S, Bai D S. Control charts for positively skewed populations with weighted standard deviations[J]. Quality and Reliability Engineering International, 2001, 17: 397-406.
[8] Chen YK. Economic design of control charts for non-normal data using variable sampling policy[J]. International Journal of Production Economics, 2004, 92: 61-74.
[9] Lorenzen T J, Vance L C. The economic design of control charts: a unified approach[J]. Technometrics, 1986, 28(1): 3-10.
[10] Chou CY, Cheng J C, Lai W T. Economic design of variable sampling intervals EWMA charts with sampling at fixed times using genetic algorithms[J]. Expert Systems with Applications, 2008, 34: 419-426.
[11] 薛丽.可变抽样区间几何EWMA控制图的经济设计[J].运筹与管理,2013,22(4):126-132.
[12] 薛丽.监控均值标准差的可变抽样区间EWMA图经济设计[J].计算机集成制造系统,2013,19(6):1369-1376.

可变抽样区间和样本容量的非正态EWMA控制图经济设计

Economic Design of Variable Sampling Interval and Sample Size EWMA Control Chart under Non-normal Distributions

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[1]	薛丽. 基于预防维修和质量损失函数的VSI EWMA控制图经济设计[J]. 运筹与管理, 2020, 29(2): 116-128.
[2]	薛丽. 可变抽样区间几何EWMA控制图的经济设计[J]. 运筹与管理, 2013, 22(4): 126-132.