The Generally Weighted Moving Average Median Control Chart

Abstract

A generally weighted moving average median (GWMA-X̃) control chart for monitoring the process sample median is proposed. In contrast to the mean control charts, the median control charts are outlier-resistant and are easier to do on the shop floor. Developing an effective median control chart for monitoring the small shifts of the process sample median has the practical necessity. When the adjustment parameter α = 1, the GWMA-X̃ control chart reduces to the EWMA-X̃ control chart. When the design parameter q = 0, the EWMA-X̃ control chart reduces to the Shewhart-X̃ control chart. The properties and design strategies of the GWMA-X̃ control chart are investigated. The numerical simulation is used to evaluate the average run lengths of the GWMA-X̃ control chart, the EWMA-X̃ control chart and the Shewhart-X̃ control chart. After an extensive comparison, it reveals that the GWMA-X control chart outperforms both the EWMA-X̃ control chart and the Shewhart-X̃ control chart in detecting small shifts of the process sample median. An example is also given to illustrate this study.

Key Words:

• Average run length
• control chart
• EWMA
• generally weighted moving average
• median
• robustness

Additional information

Notes on contributors

Shey-Huei Sheu

Shey-Huei Sheu is a Professor in the Department of Industrial Management at National Taiwan University of Science and Technology. He received his MS degree in Applied Mathematics from National Tsing Hua University, and Ph.D. degree in Statistics from University of Kentucky. He has published numerous papers in journals such as Naval Research Logistics, Journal of Applied Probability, RAIOR Operations Research, Microelectronics & Reliability, Reliability Engineering & System Safety, International Journal of System Science, International Journal of Reliability, Quality and Safety Engineering, Journal of the Operational Research Society, European Journal Operational Research, IEEE Transactions on Reliability, Production Planning & Control, Computers & Operations Research, Quality Engineering, and Annuals of Operations Research.

Ling Yang

Ling Yang is an Associate Professor in the Department of Industrial Engineering and Management at St. John’s University, Taiwan. She received her MS degree in Management Science from National Chiao Tung University, Taiwan, and Ph.D. degree in Management Science from National Taiwan University of Science and Technology.