A synthetic exponentially weighted moving average control chart to monitor process median based on ranked set sampling

Department of Mathematical and Actuarial Sciences, Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, 43000 Kajang, Selangor, Malaysia

^* Corresponding author: ngjw@utar.edu.my

Abstract

Exponentially Weighted Moving Average (EWMA) control charts yield insights into data in a way more comprehensible to the practitioners and researchers because of its capability in discovering small to moderate process mean shifts. EWMA control chart is incorporated with conforming run length (CRL) chart, named synthetic EWMA chart, to enhance the performance of the chart in detecting the out-of-control signal. Synthetic EWMA chart based on ranked set sampling (RSS) for monitoring process mean has been proposed as it advanced the detection of chart over a series of mean shifts. With the situation that normality assumption is scarcely attain in practice, we proposed synthetic EWMA median chart based on RSS. Rather than select average run length (ARL) as sole performance evaluating tool, the median and percentiles of run-length distribution are used to examine the performance of the proposed chart as it provides more information on the entire run-length distribution. Near-optimal parameters of the proposed chart will be acquired by setting the incontrol ARL at a designated value. The run length performances of the proposed chart are then compared with the existing charts such as EWMA median chart based on RSS.