The Measurement Errors and Their Effects on the Cumulative Sum Schemes for Monitoring the Ratio of Two Correlated Normal Variables

Author:

Yang Wei12,Ji Xueting3,Zhang Jiujun1

Affiliation:

1. School of Mathematics and Statistics, Liaoning University, Shenyang 110036, China

2. School of Mathematics and Information Science, Anshan Normal University, Anshan 114007, China

3. School of Economics and Law, University of Science and Technology Liaoning, Anshan 114051, China

Abstract

Monitoring the ratio of two correlated normal random variables is often used in many industrial manufacturing processes. At the same time, measurement errors inevitably exist in most processes, which have different effects on the performance of various charting schemes. This paper comprehensively analyses the impacts of measurement errors on the detection ability of the cumulative sum (CUSUM) charting schemes for the ratio of two correlated normal variables. A thorough numerical assessment is performed using the Monte Carlo simulation, and the results indicate that the measurement errors negatively impact the performance of the CUSUM scheme for the ratio of two correlated normal variables. Increasing the number of measurements per set is not a lucrative approach for minimizing the negative impact of measurement errors on the performance of the CUSUM charting scheme when monitoring the ratio of two correlated normal variables. We consider a food formulation as an example that illustrates the quality control problems involving the ratio of two correlated normal variables in an industry with a measurement error. The results are presented, along with some suggestions for further study.

Funder

National Natural Science Foundation of China

esearch on Humanities and Social Sciences of the Ministry of Education

Doctoral Research Start-up Fund of Liaoning Province

Education Department of Liaoning Province

Liaoning Provincial Department of Education Scientific Research Project

Research Project of Anshan Normal University

Publisher

MDPI AG

Reference41 articles.

1. Montgomery, D.C. (2009). Introduction to Statistical Quality Control, John Wiley & Sons. [6th ed.].

2. Qiu, P. (2014). Introduction to Statistical Process Control, Chapman & Hall/CRC.

3. Shewhart, W.A. (1931). Economic Control of Quality of Manufactured Product, D. Van Nostrand Company.

4. Continuous inspection schemes;Page;Biometrika,1954

5. Control chart tests based on geometric moving averages;Roberts;Technometrics,1959

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