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基于平方秩和的变点控制图的生产提前期控制研究

仲建兰,江天,赵宏伟   

  1. 福建农林大学经济管理学院, 福州 350002
  • 出版日期:2018-04-25 发布日期:2021-06-29

仲建兰, 江天, 赵宏伟. 基于平方秩和的变点控制图的生产提前期控制研究[J]. 系统科学与数学, 2021, 41(4): 1079-1090.

ZHONG Jianlan , JIANG Tian , ZHAO Hongwei. A Change Point Control Chart for Monitoring the Production Lead Time Based on Sum of Squared Ranks[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(4): 1079-1090.

A Change Point Control Chart for Monitoring the Production Lead Time Based on Sum of Squared Ranks

ZHONG Jianlan ,JIANG Tian , ZHAO Hongwei   

  1. School of Economics and Management, Fujian Agriculture and Forestry University, Fuzhou 350002
  • Online:2018-04-25 Published:2021-06-29
将串并联加工系统看做$M/G/m$ 的排队系统, 针对服务时间概 率分布不确定的情形, 以生产提前期为监控对象, 基于平方秩和设计变点 控制图. 首先, 以订单在某阶段的逗留时间为状态变量采用状态空间方程 对该系统进行建模, 并分析逗留时间均值发生偏移对下游工序的影响. 其次, 针对服务时间服从一般分布的情形计算平均等待时间和平均逗留时间, 并基于 ~Laplace-Stieltjes (LS) 变换推算逗留时间的分布函数. 再次, 基于平方秩和设计变点控制图以监 测生产提前期. 最后, 以平均运行链长、变点估计及其所在工序估计的准确性作 为评价准则, 假设服务时间分别服从正态分布、对数正态分布、伽马分布和均匀 分布, 通过仿真分析来评价该变点控制图的监控性能. 仿真结果显示基于平方秩 和的变点控制图能有效检测系统的冗余订单, 并且较为准确地检测出过程变点以及 变点所在的工序, 且效果较为稳健. 验证了变点控制图的非参数属性. 进 一步地, 通过与加权标准差控制图进行比较分析, 结果显示所提变点控制图具有较好 的监控性能.
A serial-parallel system be viewed as an $M/G/m$ queuing system, a change point control chart based on sum of squared ranks is designed with production lead time as monitor object, for the case of uncertain probability distribution of service time. Firstly, taking sojourn time of the order at one stage as the state variable, the system is modeled by the state space equation, and the influence of the deviation of the mean sojourn time in current stage on the downstream stages is analyzed. Secondly, the average sojourn time is calculated, and the distribution function of the sojourn time is estimated based on the LS transform. Again, a change point control chart is designed based on the sum of squared ranks; and the Monte Carlo simulation is used to obtain the appropriate control limit. Finally, the average running length, the accuracy of the change point estimation and the out-of-control process estimation are used as the evaluation criteria, and the simulation analysis is used to evaluate the monitoring performance of the change point control chart. The results show the change point control chart can effectively detect the mean shift of lead time, and accurately estimate the change point and its out-of-control stage. Its effect is more robust for four studied distribution. In addition, by comparing with the weighted standard deviation control chart, the results indicate that the proposed change point control chart has better monitoring performance.
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