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On Phase-I Monitoring of Process Location Parameter with Auxiliary Information-Based Median Control Charts

Shahid Hussain (), Sun Mei (), Muhammad Riaz () and Saddam Akber Abbasi ()
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Shahid Hussain: Faculty of Science, Institute of Applied Systems Analysis, Jiangsu University, Zhenjiang 212013, China
Sun Mei: Faculty of Science, Institute of Applied Systems Analysis, Jiangsu University, Zhenjiang 212013, China
Muhammad Riaz: Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Saddam Akber Abbasi: Department of Mathematics, Statistics, and Physics, Qatar University, Doha 2713, Qatar

Mathematics, 2020, vol. 8, issue 5, 1-21

Abstract: A control chart is often used to monitor the industrial or services processes to improve the quality of the products. Mostly, the monitoring of location parameters, both in Phase I and Phase II, is done using a mean control chart with the assumption that the process is free from outliers or the estimators are correctly estimated from in-control samples. Generally, there are question marks about such kind of narratives. The performance of the mean chart is highly affected in the presence of outliers. Therefore, the median chart is an attractive alternative to the mean chart in this situation. The control charts are usually implemented in two phases: Phase I (retrospective) and Phase II (prospective/monitoring). The efficiency of any control chart in Phase II depends on the accuracy of control limits obtained from Phase I. The current study focuses on the Phase I analysis of location parameters using median control charts. We examined the performance of different auxiliary information-based median control charts and compared the results with the usual median chart. Standardized variance and relative efficacy are used as performance measures to evaluate the efficiency of median estimators. Moreover, the probability to signal measure is used to evaluate the performance of proposed control charts to detect any potential changes in the process. The results revealed that the proposed auxiliary information based median control charts perform better in Phase I analysis. In addition, a practical illustration of an industrial scenario demonstrated the significance of the proposed control charts, in which the monitoring of concrete compressive strength is emphasized.

Keywords: auxiliary information; median control charts; Phase I monitoring; probability to signal; relative efficiency; standardized variance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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