Abstract

Assuming that a two-stage serial-parallel processing system is an M/G/m queuing system. Firstly, let sojourn time of the order in one stage is the system state, and the state space equation is used to model this system. Also, the influence of the mean shift of sojourn time on the downstream stage is analyzed. Secondly, the average sojourn time is calculated. And the distribution function of the sojourn time is estimated based on the Laplace-Stieltjes (LS) transformation. Thirdly, a change point control chart is designed based on the sum of squared ranks to monitor back order. Finally, the performance of the change point control chart is evaluated via simulation in terms of average run length, the accuracy of the change point estimation and the out-of-control stage estimation. The results show that the change point control chart can effectively detect the mean shift of the lead time, and it can estimate the change point and its out-of-control stage more accurately.

摘要

假设两级串并处理系统是M/G/m排队系统。首先，令某一阶段的阶次停留时间为系统状态，利用状态空间方程对该系统进行建模。同时，分析了滞留时间均值漂移对下游阶段的影响。其次，计算平均逗留时间。并且逗留时间的分布函数是基于拉普拉斯-斯蒂尔捷斯（LS）变换估计的。第三，设计了一个基于秩和的变化点控制图来监控延迟订单。最后，通过仿真从平均运行长度、变化点估计的准确性和失控阶段估计的角度来评估变化点控制图的性能。