A change point control chart for monitoring the production lead time based on sum of squared ranks. Issue 11 (2nd November 2022) - Zhong, Jianlan; Hu, Xulong; Jiang, Tian
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.