Outliers Detection Models in Shewhart Control Charts; an Application in Photolithography: A Semiconductor Manufacturing Industry

Ishaq Adeyanju Raji, Muhammad Hisyam Lee, Muhammad Riaz, Mu’azu Ramat Abujiya and Nasir Abbas
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Ishaq Adeyanju Raji: Department of Mathematical Sciences, Universiti Teknologi Malaysia, Skudai 81310, Malaysia
Muhammad Hisyam Lee: Department of Mathematical Sciences, Universiti Teknologi Malaysia, Skudai 81310, Malaysia
Muhammad Riaz: Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Mu’azu Ramat Abujiya: Preparatory Year Mathematics Program, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
Nasir Abbas: Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Mathematics, 2020, vol. 8, issue 5, 1-17

Abstract: Shewhart control charts with estimated control limits are widely used in practice. However, the estimated control limits are often affected by phase-I estimation errors. These estimation errors arise due to variation in the practitioner’s choice of sample size as well as the presence of outlying errors in phase-I. The unnecessary variation, due to outlying errors, disturbs the control limits implying a less efficient control chart in phase-II. In this study, we propose models based on Tukey and median absolute deviation outlier detectors for detecting the errors in phase-I. These two outlier detection models are as efficient and robust as they are distribution free. Using the Monte-Carlo simulation method, we study the estimation effect via the proposed outlier detection models on the Shewhart chart in the normal as well as non-normal environments. The performance evaluation is done through studying the run length properties namely average run length and standard deviation run length. The findings of the study show that the proposed design structures are more stable in the presence of outlier detectors and require less phase-I observation to stabilize the run-length properties. Finally, we implement the findings of the current study in the semiconductor manufacturing industry, where a real dataset is extracted from a photolithography process.

Keywords: average run length; control chart; median absolute deviation; outlier; photolithography; Shewhart; Tukey (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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