Optimal Design of the Synthetic Median Chart Based on Average Run Length and Expected Average Run Length  
Author XueLong Hu


Co-Author(s) Shu Wu; JianLan Zhong


Abstract Considering the sensitive property of the sample mean to outliers in observations, the median X~chart is preferred to the mean X¯ chart. Under such situation, a synthetic chart for the process median is proposed in this paper. The run length properties of the synthetic median chart are examined using a Markov chain approach, and the chart parameters are provided for different combinations of mean shift δ and sample size n with a fixed incontrol ARL (average run length) performance. To deal with the random shift size problem, we also presented an methodology to design the synthetic median chart based on the integration of ARL over the distribution of different mean shift domain. The simulation results showed that the proposed chart’s performance are better than the traditional median chart, especially for smaller to moderate shifts.


Keywords Average run length, Standard deviation of the run length, Shewhart median chart, Synthetic median chart, EWMA median
    Article #:  24197
Proceedings ISSAT International Conference on Reliability and Quality in Design 2018
August 2-4, 2018 - Toronto, Ontario, Canada